classical and motivic adams charts
TRANSCRIPT
Wayne State University
Mathematics Research Reports Mathematics
12-1-2014
Classical and Motivic Adams ChartsDaniel C. IsaksenWayne State University, [email protected]
This Technical Report is brought to you for free and open access by the Mathematics at DigitalCommons@WayneState. It has been accepted forinclusion in Mathematics Research Reports by an authorized administrator of DigitalCommons@WayneState.
Recommended CitationIsaksen, Daniel C., "Classical and Motivic Adams Charts" (2014). Mathematics Research Reports. Paper 94.http://digitalcommons.wayne.edu/math_reports/94
CLASSICAL AND MOTIVIC ADAMS CHARTS
DANIEL C. ISAKSEN
Abstract. This document contains large-format Adams charts that compute 2-complete stable homotopy groups,both in the classical context and in the motivic context over C. The charts are essentially complete throughthe 59-stem and contain partial results to the 70-stem. In the classical context, we believe that these are the mostaccurate charts of their kind.
We also include Adams charts for the motivic homotopy groups of the cofiber of τ .
This document contains large-format Adams charts that compute 2-complete stable homotopy groups,both in the classical context and in the motivic context over C. The charts are essentially complete throughthe 59-stem and contain partial results to the 70-stem. In the classical context, we believe that these are themost accurate charts of their kind.We also include Adams charts for the motivic homotopy groups of the cofiber of τ .The charts are intended to be viewed electronically. The author can supply versions that are suitable for
printing.Justifications for these calculations appear in [1].
1. The classical Adams spectral sequence
This chart shows the classical Adams spectral sequence. The E2-page is complete through the 70-stem, asare the Adams d2 differentials. The Adams d3, d4, and d5 differentials are complete through the 65-stem,with a few indicated exceptions.
(1) Black dots indicate copies of F2.(2) Vertical lines indicate h0 multiplications.(3) Lines of slope 1 indicate h1 multiplications.(4) Lines of slope 1/3 indicate h2 multiplications.(5) Light blue lines of slope −2 indicate Adams d2 differentials.(6) Red lines of slope −3 indicate Adams d3 differentials.(7) Green lines of slope −4 indicate Adams d4 differentials.(8) Blue lines of slope −5 indicate Adams d5 differentials.(9) Dashed lines indicate plausible Adams d3, d4, and d5 differentials, but we have not independently
verified their existence.
2. The E∞-page of the classical Adams spectral sequence
This chart indicates the E∞-page of the classical Adams spectral sequence. The chart is essentiallycomplete through the 59-stem. Because of unknown differentials, the actual E∞-page beyond the 59-stem isa subquotient of what is shown.See Section 1 for instructions on interpreting the chart. In addition:
(1) Olive lines indicate hidden 2 extensions.(2) Purple lines indicate hidden η extensions.(3) Brown lines indicate hidden ν extensions.(4) Dashed olive, purple, and brown lines indicate possible hidden extensions.(5) For clarity, some of the unknown Adams d3, d4, and d5 differentials are also shown on this chart.
3. The cohomology of the motivic Steenrod algebra
This chart shows the cohomology of the motivic Steenrod algebra over C. The chart is complete throughthe 70-stem.
(1) Black dots indicate copies of M2.(2) Red dots indicate copies of M2/τ .(3) Blue dots indicate copies of M2/τ
2.(4) Green dots indicate copies of M2/τ
3.(5) Vertical lines indicate h0 multiplications. These lines might be black, red, blue, or green, depending
on the τ torsion of the target.(6) Lines of slope 1 indicate h1 multiplications. These lines might be black, red, blue, or green, depending
on the τ torsion of the target.(7) Lines of slope 1/3 indicate h2 multiplications. These lines might be black, red, blue, or green,
depending on the τ torsion of the target.(8) Red arrows indicate infinite towers of h1 multiplications, all of which are annihilated by τ .(9) Magenta lines indicate that an extension hits τ times a generator. For example, h0 · h0h2 = τh3
1 inthe 3-stem.
(10) Orange lines indicate that an extension hits τ2 times a generator. For example, h0 · h30x = τ2h0e0g
in the 37-stem.(11) Dotted lines indicate that the extension is hidden in the May spectral sequence.(12) Squares indicate that there is a τ extension that is hidden in the May spectral sequence. For example,
τ · Pc0d0 = h50r in the 30-stem.
4. The E2-page of the motivic Adams spectral sequence
This chart indicates the Adams d2 differentials on the E2-page of the motivic Adams spectral sequence.The chart is complete through the 70-stem. See Section 3 for instructions on interpreting the chart. Inaddition:
(1) Blue lines of slope −2 indicate Adams d2 differentials.(2) Magenta lines of slope −2 indicate that an Adams d2 differential hits τ times a generator. For
example, d2(h0c2) = τh21e1 in the 40-stem.
(3) Orange lines of slope −2 indicate that an Adams d2 differential hits τ2 times a generator. Forexample, d2(h0y) = τ2h0e0g in the 37-stem.
5. The E3-page of the motivic Adams spectral sequence
This chart indicates the Adams d3 differentials on the E3-page of the motivic Adams spectral sequence.The chart is complete through the 65-stem, with indicated exceptions. Beyond the 65-stem, there are severalunknown differentials.See Section 3 for instructions on interpreting the chart. In addition:
(1) Blue lines of slope −3 indicate Adams d3 differentials.(2) Magenta lines of slope −3 indicate that an Adams d3 differential hits τ times a generator. For
example, d3(r) = τh1d20 in the 29-stem.
(3) Orange lines of slope −3 indicate that an Adams d3 differential hits τk times a generator for k ≥ 2.For example, d3(Q2) = τ2gt in the 56-stem, and d3(τW1) = τ4e40 in the 68-stem.
(4) Dashed lines indicate plausible Adams d3 differentials, but we have not independently verified theirexistence.
2000 Mathematics Subject Classification. 55T15, 55Q45, 14F42.Key words and phrases. Adams spectral sequence, stable homotopy group, motivic stable homotopy group.The author was supported by NSF grant [email protected]
Department of Mathematics, Wayne State University, Detroit, MI 48202.
6. The E4-page of the motivic Adams spectral sequence
This chart indicates the Adams d4 and d5 differentials on the E4-page of the motivic Adams spectralsequence. The chart is complete through the 65-stem, with a few indicated exceptions. Beyond the 65-stem,there are several unknown differentials.Because of unknown d3 differentials, the actual E4-page beyond the 65-stem is a subquotient of what is
shown.See Section 3 for instructions on interpreting the chart. In addition:
(1) Purple dots indicate copies of M2/τ4.
(2) Blue lines of slope −4 and −5 indicate Adams d4 and d5 differentials.(3) Magenta lines of slope −5 indicate that an Adams d5 differential hits τ times a generator. For
example, d5(τPh5e0) = τd0z in the 55-stem.(4) Orange lines of slope −4 and −5 indicate that an Adams d4 or d5 differential hits τ
k times a generatorfor k ≥ 2.
(5) Dashed lines indicate plausible Adams d3, d4, and d5 differentials, but we have not independentlyverified their existence.
(6) For clarity, the unknown Adams d3 differentials are also shown on this chart.
7. The E∞-page of the motivic Adams spectral sequence
This chart indicates the E∞-page of the motivic Adams spectral sequence. The chart is complete throughthe 59-stem. Because of unknown differentials, the actual E∞-page beyond the 59-stem is a subquotient ofwhat is shown.See Section 3 for instructions on interpreting the chart. In addition:
(1) Purple dots indicate copies of M2/τ4.
(2) For clarity, some of the unknown Adams d3, d4, and d5 differentials are also shown on this chart.
8. The E2-page of the motivic Adams spectral sequence for the cofiber of τ
This chart indicates the E2-page of the motivic Adams spectral sequence for the cofiber of τ . The chart iscomplete through the 70-stem, with indicated exceptions.
(1) Black dots indicate copies of M2/τ that are in the image of the inclusion E2(S0,0) → E2(Cτ) of the
bottom cell.(2) Red dots indicate copies of M2/τ that are detected by the projection E2(Cτ) → E2(S
0,0) to the topcell.
(3) Black lines indicate extensions by h0, h1, and h2 that are in the image of the inclusion of the bottomcell.
(4) Red lines indicate extensions by h0, h1, and h2 that are detected by projection to the top cell.(5) Blue lines indicate extensions by h0, h1, and h2 that are hidden in the sense that they are not
detected by the top cell or the bottom cell.(6) Arrows of slope 1 indicate infinite towers of h1 extensions.(7) Dashed blue lines indicate unknown hidden extensions.(8) Light blue lines indicate Adams differentials.(9) Dashed light blue lines indicate unknown Adams differentials. These unknown differentials are also
indicated on later charts.
9. The E3-page of the motivic Adams spectral sequence for the cofiber of τ
This chart indicates the E3-page of the motivic Adams spectral sequence for the cofiber of τ . The E3-pageis complete through the 70-stem, but the Adams d3 differentials are complete only through the 64-stem.Beyond the 64-stem, there are a number of unknown differentials.See Section 8 for instructions on interpreting the chart.
10. The E4-page of the motivic Adams spectral sequence for the cofiber of τ
This chart indicates the E4-page of the motivic Adams spectral sequence for the cofiber of τ . The E4-pageis complete through the 64-stem. Beyond the 64-stem, the actual E4-page is a subquotient of what is shown.The chart shows both Adams d4 and d5 differentials.See Section 8 for instructions on interpreting the chart.
11. The E∞-page of the motivic Adams spectral sequence for the cofiber of τ
This chart indicates the E∞-page of the motivic Adams spectral sequence for the cofiber of τ . The chartis complete through the 63-stem, but hidden extensions are only shown through the 59-stem. Beyond the63-stem, the actual E∞-page is a subquotient of what is shown.
(1) Black dots indicate copies of M2/τ that are in the image of the inclusion π∗,∗ → π∗,∗(Cτ) of thebottom cell.
(2) Red dots indicate copies of M2/τ that are detected by the projection π∗,∗(Cτ) → π∗−1,∗+1 to thetop cell.
(3) Black lines indicate extensions by h0, h1, and h2 that are in the image of the inclusion of the bottomcell.
(4) Red lines indicate extensions by h0, h1, and h2 that are detected by projection to the top cell.(5) Blue lines indicate extensions by 2, η, and ν that are not hidden in the E∞-page but are not detected
by the top cell or the bottom cell.(6) Arrows of slope 1 indicate infinite towers of h1 extensions.(7) Olive lines indicate 2 extensions that are hidden in the E∞-page.(8) Purple lines indicate η extensions that are hidden in the E∞-page.(9) Brown lines indicate ν extensions that are hidden in the E∞-page.(10) Dashed lines indicate possible extensions.(11) Dashed light blue lines indicate unknown Adams differentials. These unknown differentials are
included for clarity.
References
[1] Daniel C. Isaksen, Stable stems (2014), preprint, available at arXiv:1407.8418.
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The classical Adams spectral sequence
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70
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2
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8
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12
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h0 h1 h2 h3
c0
Ph1 Ph2
h2
3
d0
h4
Pc0
e0
P 2h1
f0
c1
P 2h2
g
Pd0
h4c0
i
P 2c0
Pe0
P 3h1
j
P 3h2
d2
0
k
h2
4
r
P 2d0
h5
n
d0e0 + h7
0h5
d1
q
l
P 3c0
p
P 2e0
P 4h1
e20
Pj
m
P 4h2
t
Pd2
0
x
e0g
d0i
h3h5
e1
y
P 3d0
h5c0
u
Pd0e0
P 2i
f1
Ph1h5
g2
d0j
P 4c0
c2
z
P 3e0
P 5h1
Ph2h5
v
d3
0
P 2j
d0k
P 5h2
g2
d0r
P 2d2
0
h2
3h5
h5d0
w
d2
0e0
Pd0i
B1
N
d0l
i2
P 4d0
Ph5c0
e0r
Q′ Pu
P 2d0e0
h3c2
h5e0
B2
d0e2
0
Pd0j
P 5c0
h5f0
d0m
ij
P 4e0
P 6h1
h5c1
C
gr
Pv
Pd3
0
P 3j
h3g2
gn
d0e0g
d2
0i
P 6h2
D1
d1g
e0m
Pd0r
P 3d2
0
Ph5d0
x′
d0u
Pd2
0e0
P 2d0i
G
h5i
R1
e20g
d2
0j + h5
0R1
P 5d0
gm
il
P 2u
P 3d0e0
P 4i
Ph5e0
Q1
gt
d0v
d4
0
P 2d0j
P 6c0
Q2
h5j
e0g2
Pd0m
Pij
P 5e0
P 7h1
D2
d2
0r
P 2v
P 2d3
0
P 4j
B21
e0v
d3
0e0
Pd2
0i
P 7h2
B3
B4
g3
d2
0l
d0i2
P 4d2
0
D3
A′
A+A′
X1
nr
jm
Pd0u
P 2d2
0e0
P 3d0i
h2
5
H1
h5n
E1
E1+C0
RB22
gv
Ph1x′
d2
0e20
Pd2
0j + h9
0R
P 2i2
P 6d0
h6
X2C′
d2
0m
d0ij
P 3u
P 4d0e0
A′′
h3Q2
q1
Ud0gr
Pd0v
Pd4
0
P 3d0j
P 7c0
h3D2
B23
Ph5j
R2gw
d0e3
0
P 2d0m
P 2ij
P 6e0
P 8h1
r1
G0
B5
D′
2
nm
d0e0m
Pd2
0r
P 3v
P 3d3
0
P 5j
n1
Q3
X3C′′
C11
d0x′lm
d2
0u
Pd3
0e0
P 2d2
0i
P 8h2
d2
h3(A+A′)
G21
G11
e40
d3
0j
Pd0i2
P 5d2
0
p′
h3H1
D′
3
P (A+A′)
W1
d0gm
P 2x′
d2
0z
P 2d0u
P 3d2
0e0
P 4d0i
h3h6
p1
d1e1
m2
e0x′
R′
1
d2
0v
d5
0
P 2d2
0j + h6
0R′
1
P 7d0
3
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 350
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The E∞-page of the classical Adams spectral sequence
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70
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4
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h0 h1 h2 h3
c0
Ph1 Ph2
h2
3
d0 h3
0h4
h1h4
Pc0
P 2h1
h2h4
c1
P 2h2
g
Pd0
h4c0
h2
0i
P 2c0
P 3h1 P 3h2
d2
0
h2
4
n
h10
0h5
h1h5
d1
q
P 3c0
p
P 4h1
h0h2h5
e20
P 4h2
t
h2
2h5
x
h2
0h3h5
h1h3h5
h5c0
h3d1
u
P 2h2
0i
f1
Ph1h5
g2
P 4c0
z
P 5h1
Ph2h5
d3
0
P 5h2
g2
h2
3h5
h5d0
w
B1
N
d0l
Ph5c0
e0r
Pu
h7
0Q′
B2
d0e2
0
P 5c0
P 6h1
h5c1
C
h3g2
gn
P 6h2
d1g
e0m
x′
d0u
h0h5i
e20g
P 4h2
0i
P 6c0
P 7h1
h1Q2
B21
d0w
P 7h2
B3
g3
d2
0l
D3
A′
d0e0r
h2
5
h5n
E1 + C0
Rh1X1
d2
0e20
h1H1
X2
C′
h25
0h6
h1h6
h3Q2
q1
P 7c0
k1
B23
Ph5j
gw
P 8h1
r1
B5 + D′
2
d0e0m
Q3
X3
C11
d0x′ e0gr
d2
0u
P 8h2
d2
h2
2H1
h3A′
h3
0G21
h0h4x′
h2
2h6
p′
D′
3
h3(E1 + C0)
h3h6
p1
h2Q3
h1h3H1
d1e1
h1W1
4
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 350
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The cohomology of the motivic Steenrod algebra
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h0 h1 h2 h3
c0
Ph1 Ph2
h2
3
d0
h4
Pc0
e0
P 2h1
f0
c1
P 2h2
τg
c0d0
Pd0
h4c0
h2g
i
P 2c0
c0e0
Pe0
P 3h1
j
h3g
P 3h2
d2
0
k
h2
4
r
Pc0d0
P 2d0
h5
n
d0e0
d1
q
l
P 3c0
p
Pc0e0
P 2e0
P 4h1
e20
Pj
m
P 4h2
t
c0d2
0
Pd2
0
x
e0g
d0i
h3h5
e1
y
P 2c0d0
P 3d0
h5c0
c1g
u
c0d0e0
Pd0e0
P 2i
f1
Ph1h5
τg2
d0j
P 4c0
c2
z
P 2c0e0
P 3e0
P 5h1
Ph2h5
v
c0e2
0
d3
0
P 2j
h2g2
d0k
P 5h2
g2
d0r
Pc0d2
0
P 2d2
0
h2
3h5
h5d0
τw
c0e0g
d2
0e0
Pd0i
B1
N
d0lu′
i2
P 3c0d0
P 4d0
Ph5c0
h3g2
e0r
Q′ Pu
Pc0d0e0
P 2d0e0
h3c2
h5e0
B2
d0e2
0
Pd0j
P 5c0
h5f0
e0lv′
ij
P 3c0e0
P 4e0
P 6h1
h5c1
C
gr
Pv
c0d3
0
Pd3
0
P 3j
h3g2
G3 gn
e30
d2
0i
P 6h2
D1
d1g
e0m
ik
P 2c0d2
0
P 3d2
0
i1
h5c0d0
B8
x′
d0u
c0d2
0e0
Pd2
0e0
P 2d0i
τG
h5i
R1
e20g
d2
0j
Pu′
P 4c0d0
P 5d0
B6
gm
il
P 2u
P 2c0d0e0
P 3d0e0
P 4i
Ph5e0
Q1
gt
d0v
c0d0e2
0
d4
0
P 2d0j
P 6c0
D4
Q2
h5j
D11
τe0g2
d2
0kPv′
Pij
P 4c0e0
P 5e0
P 7h1
h2
3g2
D2
e1g
im
P 2v
Pc0d3
0
P 2d3
0
P 4j
j1
B21
c1g2
e0v
c0e3
0
d3
0e0
Pd2
0i
P 7h2
B3
B4
τg3
h0g3
d2
0l d0u
′
d0i2
P 3c0d2
0
P 4d2
0
D3
A′
A+A′
B7
X1
nr
c0x′
jm
Pd0u
Pc0d2
0e0
P 2d2
0e0
P 3d0i
h2
5
H1
h5n
E1C0
RB22
τe0w
Ph1x′
c0e2
0g
d2
0e20
Pd2
0j P 2u′
P 2i2
P 5c0d0
P 6d0
h6
X2C′
h2g3
d2
0m
e0u′
d0ij
P 3u
P 3c0d0e0
P 4d0e0
A′′
d2
1
h3Q2
q1
U km
Pd0v
c0d4
0
Pd4
0
P 3d0j
P 7c0
h3D2
k1
τB23 c0Q2
Ph5j
R2
τgw
d0e3
0
d3
0i P 2v′
P 2ij
P 5c0e0
P 6e0
P 8h1
r1
τG0
τB5
D′
2
nm
d0e0me0v
′
d0ik
P 3v
P 2c0d3
0
P 3d3
0
P 5j
n1
τQ3
h0Q3
X3C′′
C11
B8d0
h3g3
d0x′ lm
d2
0u
c0d3
0e0
Pd3
0e0
P 2d2
0i
P 8h2
d2
h3(A+A′)
G21 h3B7
h2B23
G11
e40
d3
0j
Pd0u′
P 2ik
P 4c0d2
0
P 5d2
0
p′
h3H1
h2G0
D′
3
P (A+A′)
h2B5
τW1
e20m
Pc0x′
P 2x′
d2
0z
P 2d0u
P 2c0d2
0e0
P 3d2
0e0
P 4d0i
h3h6
p1
h2Q3
d1e1
B8e0
m2
e0x′
R′
1
d2
0v
c0d2
0e20
d5
0
P 2d2
0j
P 3u′
P 6c0d0
P 7d0
5
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 350
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The E2-page of the motivic Adams spectral sequence
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h0 h1 h2 h3
c0
Ph1 Ph2
h2
3
d0
h4
Pc0
e0
P 2h1
f0
c1
P 2h2
τg
c0d0
Pd0
h4c0
h2g
i
P 2c0
c0e0
Pe0
P 3h1
j
h3g
P 3h2
d2
0
k
h2
4
r
Pc0d0
P 2d0
h5
n
d0e0
d1
q
l
P 3c0
p
Pc0e0
P 2e0
P 4h1
e20
Pj
m
P 4h2
t
c0d2
0
Pd2
0
x
e0g
d0i
h3h5
e1
y
P 2c0d0
P 3d0
h5c0
c1g
u
c0d0e0
Pd0e0
P 2i
f1
Ph1h5
τg2
d0j
P 4c0
c2
z
P 2c0e0
P 3e0
P 5h1
Ph2h5
v
c0e2
0
d3
0
P 2j
h2g2
d0k
P 5h2
g2
d0r
Pc0d2
0
P 2d2
0
h2
3h5
h5d0
τw
c0e0g
d2
0e0
Pd0i
B1
N
d0lu′
i2
P 3c0d0
P 4d0
Ph5c0
h3g2
e0r
Q′ Pu
Pc0d0e0
P 2d0e0
h3c2
h5e0
B2
d0e2
0
Pd0j
P 5c0
h5f0
e0lv′
ij
P 3c0e0
P 4e0
P 6h1
h5c1
C
gr
Pv
c0d3
0
Pd3
0
P 3j
h3g2
G3 gn
e30
d2
0i
P 6h2
D1
d1g
e0m
ik
P 2c0d2
0
P 3d2
0
i1
h5c0d0
B8
x′
d0u
c0d2
0e0
Pd2
0e0
P 2d0i
τG
h5i
R1
e20g
d2
0j
Pu′
P 4c0d0
P 5d0
B6
gm
il
P 2u
P 2c0d0e0
P 3d0e0
P 4i
Ph5e0
Q1
gt
d0v
c0d0e2
0
d4
0
P 2d0j
P 6c0
D4
Q2
h5j
D11
τe0g2
d2
0kPv′
Pij
P 4c0e0
P 5e0
P 7h1
h2
3g2
D2
e1g
im
P 2v
Pc0d3
0
P 2d3
0
P 4j
j1
B21
c1g2
e0v
c0e3
0
d3
0e0
Pd2
0i
P 7h2
B3
B4
τg3
h0g3
d2
0l d0u
′
d0i2
P 3c0d2
0
P 4d2
0
D3
A′
A+A′
B7
X1
nr
c0x′
jm
Pd0u
Pc0d2
0e0
P 2d2
0e0
P 3d0i
h2
5
H1
h5n
E1C0
RB22
τe0w
Ph1x′
c0e2
0g
d2
0e20
Pd2
0j P 2u′
P 2i2
P 5c0d0
P 6d0
h6
X2C′
h2g3
d2
0m
e0u′
d0ij
P 3u
P 3c0d0e0
P 4d0e0
A′′
d2
1
h3Q2
q1
U km
Pd0v
c0d4
0
Pd4
0
P 3d0j
P 7c0
h3D2
k1
τB23 c0Q2
Ph5j
R2
τgw
d0e3
0
d3
0i P 2v′
P 2ij
P 5c0e0
P 6e0
P 8h1
r1
τG0
τB5
D′
2
nm
d0e0me0v
′
d0ik
P 3v
P 2c0d3
0
P 3d3
0
P 5j
n1
τQ3
h0Q3
X3C′′
C11
B8d0
h3g3
d0x′ lm
d2
0u
c0d3
0e0
Pd3
0e0
P 2d2
0i
P 8h2
d2
h3(A+A′)
G21 h3B7
h2B23
G11
e40
d3
0j
Pd0u′
P 2ik
P 4c0d2
0
P 5d2
0
p′
h3H1
h2G0
D′
3
P (A+A′)
h2B5
τW1
e20m
Pc0x′
P 2x′
d2
0z
P 2d0u
P 2c0d2
0e0
P 3d2
0e0
P 4d0i
h3h6
p1
h2Q3
d1e1
B8e0
m2
e0x′
R′
1
d2
0v
c0d2
0e20
d5
0
P 2d2
0j
P 3u′
P 6c0d0
P 7d0
6
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 350
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
The E3-page of the motivic Adams spectral sequence
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
h0 h1 h2 h3
c0
Ph1 Ph2
h2
3
d0
h0h4h1h4
Pc0
P 2h1
h2h4
c1
P 2h2
τg
h0g
c0d0
Pd0
h4c0
h2g
h2
0i
P 2c0
P 3h1 P 3h2
h1h3g
d2
0
h2
4
r
Pc0d0
P 2d0
h3
0h5
n
τd0e0
h1h5
d1
q
P 3c0
p
P 4h1
h2h5
e20
P 4h2
t
c0d2
0
Pd2
0
x
τe0g
h3h5
e1
P 2c0d0
P 3d0
h5c0
c1g
u
τPd0e0
P 2h2
0i
f1
Ph1h5
τg2
h0g2
P 4c0
z
P 5h1
Ph2h5
c0e2
0
d3
0
h2g2
P 5h2
g2
d0r
Pc0d2
0
P 2d2
0
h2
3h5
h5d0
τw
τd2
0e0
B1
N
τd0l + u′
i2
P 3c0d0
P 4d0
Ph5c0
e0r
Pu
τP 2d0e0
h5
0Q′
B2
h1h3g2
d0e2
0
P 5c0
h1h5e0
τ2d0m
ij
P 6h1
h5c1
C
gr
c0d3
0
Pd3
0
h3g2
gn
τd0e0g
P 6h2
d1g
h1G3
τ2e0m
Pd0r
P 2c0d2
0
P 3d2
0
i1
B8
x′
d0u
τPd2
0e0
τ2G
h5i
τe20g
Pu′ + τd2
0j
P 4c0d0
P 5d0
B6
τ2gm
d0z
P 2u
τP 3d0e0
P 4h2
0i
h5c0e0
Ph5e0
gt
τd0v
c0d0e2
0
d4
0
P 6c0
Q2
h5j
D11
τe0g2
h2e2
0g
τ2Pd0m
Pij
P 7h1
h2
3g2
e1g
d2
0r
Pc0d3
0
P 2d3
0
j1
B21
c1g2
τd0w
τd3
0e0
P 7h2
B3
h3
1D4
τg3
h0g3
d0u′ + τd2
0l
d0i2
P 3c0d2
0
P 4d2
0
D3
A′
nr
c0x′
d0e0r
Pd0u
τP 2d2
0e0
h2
5
h5n
E1
C0
Rh1X1 + τB22
τh1X1
τgv
Ph1x′
d2
0e20
P 2u′ + τPd2
0j
P 2i2
P 5c0d0
P 6d0
τh1H1
τX2
C′
h7
0h6
h2g3
τ2d2
0m
d0ij
P 3u
τP 4d0e0
h1h6
d2
1
h3Q2
q1
e20r
τPd0v
c0d4
0
Pd4
0
P 7c0
k1
h2
1X2
c0Q2τB23
h2B22
Ph5j
τgw
τd0e3
0
τ2P 2d0m
P 2ij
P 8h1
r1
τ2B5 + D′
2
nm
τ2d0e0m
Pd2
0r
P 2c0d3
0
P 3d3
0
τQ3
h0Q3
X3C′′
C11
B8d0
d0x′ e0gr
d2
0u
τPd3
0e0
P 8h2
d2
h2
2H1
h3A′
h2B23
τh3
0G21
h0h4x′
h1h3g3
e40
Pd0u′ + τd3
0j
Pd0i2
P 4c0d2
0
P 5d2
0
h2
2h6
p′
τD′
3
h3E1
h2B5
τW1
τ2d0gm
Pc0x′
P 2x′
d2
0z
P 2d0u
τP 3d2
0e0
h3h6
p1
h2Q3
τh1h3H1
d1e1
m2τe0x
′
τd2
0v
c0d2
0e20
d5
0
P 3u′ + τP 2d2
0j
P 6c0d0
P 7d0
7
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 350
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
The E4-page of the motivic Adams spectral sequence
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
h0 h1 h2 h3
c0
Ph1 Ph2
h2
3
d0 h3
0h4
h1h4
Pc0
P 2h1
h2h4
c1
P 2h2
τg
h0g
c0d0
Pd0
h4c0
h2g
h2
0i
P 2c0
P 3h1 P 3h2
h1h3g
d2
0
h2
4
P 2d0
n
τ2d0e0 + h7
0h5
h1h5
d1
q
P 3c0
p
P 4h1
h0h2h5
e20
P 4h2
t
Pd2
0
h2
2h5
x
τ2e0g
h3h5
P 3d0
h5c0
h3d1
c1g
u
τ2Pd0e0
P 2h2
0i
f1
Ph1h5
τg2
h0g2
P 4c0
z
P 5h1
Ph2h5
c0e2
0
d3
0
h2g2
P 5h2
g2
P 2d2
0
h2
3h5
h5d0
τw
τ2d2
0e0
B1
N
τd0l + u′
P 4d0
Ph5c0
e0r
Pu
τ2P 2d0e0
h7
0Q′
B2
h1h3g2
d0e2
0
P 5c0
ij
P 6h1
h5c1
C
τ2gr
Pd3
0
h3g2
gn
τ2d0e0g
P 6h2
d1g
h1G3
τ2e0m
P 3d2
0
i1
B8
x′
d0u
τ2Pd2
0e0
h0h5i
h6
1h5e0
τe20g
Pu′ + τd2
0j
P 5d0
τ3gm
d0z
P 2u
τ2P 3d0e0
P 4h2
0i
τPh5e0
gt
τ2d0v
d4
0
P 6c0
D11
τ2e0g2
h2e2
0g
Pij
P 7h1
h2
3g2
h1Q2
τ2d2
0r
P 2d3
0
j1
h3d1g
B21
c1g2
Ph3
1h5e0
τd0w
τ2d3
0e0
P 7h2
B3
h3
1D4
τg3 + h4
1h5c0e0
h0g3
d0u′ + τd2
0l
P 4d2
0
D3
A′
d0e0r
Pd0u
τ2P 2d2
0e0
h2
5
h5n
E1 + C0
Rτh1X1
τ2gv
Ph1x′
d2
0e20
P 2u′ + τPd2
0j
P 2h0i2
P 6d0
τh1H1
τX2
C′
τ2h1B22
h2g3
τ3d2
0m
d0ij
h18
0h6
P 3u
h1h6
d2
1h3Q2
q1
τ2d0gr
τ2Pd0v
Pd4
0
τ2P 4h1d0e0
P 7c0
k1
h2
1X2
c0Q2τB23
h2B22
Ph5j
τgw + h4
1X1
τ2d0e3
0
P 2ij
P 8h1
r1
τ2B5 + D′
2
τ2d0e0m
τ2Pd2
0r
P 3d3
0
τQ3
h0Q3
X3
C11
B8d0
d0x′ e0gr
d2
0u
τ2Pd3
0e0
P 8h2
d2
h2
2H1
h3A′
h2B23
τh3
0G21
h0h4x′
h1h3g3
e40
Pd0u′ + τd3
0j
P 5d2
0
h2
2h6
p′
τD′
3
h3(E1 + C0)
τh2B5
τ3d0gm
P 2x′
d2
0z
P 2d0u
τ2P 3d2
0e0
h3h6
p1
h2Q3
τh1h3H1
d1e1
h2C′′
τ2m2τh1W1
τ2e0x′
τ2d2
0v
d5
0
P 3u′ + τP 2d2
0j
P 7d0
8
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 350
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
The E∞-page of the motivic Adams spectral sequence
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
h0 h1 h2 h3
c0
Ph1 Ph2
h2
3
d0 h3
0h4
h1h4
Pc0
P 2h1
h2h4
c1
P 2h2
τg
h0g
c0d0
Pd0
h4c0
h2g
h2
0i
P 2c0
P 3h1 P 3h2
h1h3g
d2
0
h2
4
n
h10
0h5
h1h5
d1
q
P 3c0
p
P 4h1
h0h2h5
e20
P 4h2
t
h2
2h5
x
h2
0h3h5
h1h3h5
h5c0
h3d1
c1g
u
P 2h2
0i
f1
Ph1h5
τg2
h0g2
P 4c0
z
P 5h1
Ph2h5
c0e2
0
d3
0
h2g2
P 5h2
g2
h2
3h5
h5d0
τw
B1
N
τd0l + u′
Ph5c0
e0r
Pu
h7
0Q′
B2
h1h3g2
d0e2
0
P 5c0
P 6h1
h5c1
C
h3g2
gn
P 6h2
d1g
h1G3
τ2e0m
i1
B8
x′
d0u
h0h5i
h6
1h5e0
τe20g
d0z
P 4h2
0i
gt
P 6c0
D11
h2e2
0g
P 7h1
h2
3g2
h1Q2
j1
h3d1g
B21
c1g2
Ph3
1h5e0
τd0w
P 7h2
B3
h3
1D4
τg3 + h4
1h5c0e0
h0g3
d0u′ + τd2
0l
D3
A′
d0e0r
h2
5
h5n
E1 + C0
Rτh1X1
d2
0e20
τh1H1
τX2
C′
τh2
1X1
h2g3
h25
0h6
h1h6
d2
1h3Q2
q1
P 7c0
k1
h2
1X2
c0Q2τB23
h2B22
Ph5j
τgw + h4
1X1
P 8h1
r1
τ2B5 + D′
2
τ2d0e0m
τQ3
h0Q3
X3
C11
B8d0
d0x′ e0gr
d2
0u
P 8h2
d2
h2
2H1
h3A′
h2B23
τh3
0G21
h0h4x′
h1h3g3
e40
h2
2h6
p′
τD′
3
h2
2C′
h3(E1 + C0)
h3h6
p1
h2Q3
τh1h3H1
d1e1
h2C′′
τh1W1
9
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 350
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
The E2-page of the motivic Adams spectral sequence for the cofiber of τ
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
h0 h1 h2
h4
1
h3
c0
Ph1
h2
1c0
Ph2
Ph4
1
h2
3
d0
h4
Pc0
e0
P 2h1
f0
c1
d0h4
1
Ph2
1c0
P 2h2
τg
h2
1e0
P 2h4
1
c0d0
Pd0
h4c0
h2g
c0d0
i
P 2c0
c0e0
Pe0
P 3h1
h4h2
1c0
c0e0
j
h3g
Pd0h4
1
P 2h2
1c0
P 3h2
h3g
d2
0
Ph2
1e0
k
P 3h4
1
h2
4
r
Pc0d0
P 2d0
h5
n
d0e0
c0c0d0
d1
q
l
Ph1c0d0
P 3c0
p
Pc0e0
P 2e0
P 4h1
e20
d0h2
1e0
Pc0e0
Pj
h3h3g
m
P 2d0h4
1
P 3h2
1c0
P 4h2
h5h4
1
t
c0d2
0
Pd2
0
P 2h2
1e0
x
e0g
e0h2
1e0
d0c0d0
d0i
P 4h4
1
h3h5
e1
y
P 2c0d0
P 3d0
h5c0
c1g
u
c0d0e0
Pd0e0
Pc0c0d0
P 2c0d0
P 2i
f1
Ph1h5
τg2
h2
1e0g
e0c0d0
d0j
P 4c0
c2
τh0g2
z
P 2c0e0
P 3e0
P 5h1
h5h2
1c0
Ph2h5 h2
3h3g
τ2h1g2
v
c0e2
0
d3
0
Pc0c0e0
P 2c0e0
P 2j
τh2c1g
h2g2
e0c0e0
d0k h3
1u
P 3d0h4
1
P 4h2
1c0
P 5h2
g2
τ2h2g2
h1v
d0r
Pc0d2
0
P 2d2
0
P 3h2
1e0
h2
3h5
h5d0
τw
c0e0g
d2
0e0
c0d0c0d0
Pd0c0d0
Pd0i
P 5h4
1
B1
N
c0e0g
d0lu′
τh0d2
0e0
i2
P 3c0d0
P 4d0
h2
1g2
Ph5c0
h3g2
τh2
2g2
e0r u′
Q′ Pu
Pc0d0e0
P 2d0e0
P 2c0c0d0
h3c2
h5e0
B2
h3g2
d0e2
0
c0e0c0d0
Pe0c0d0
Pd0j
P 3h1c0d0
P 5c0
h5f0
e0lv′
τh0d0e2
0
ij
P 3c0e0
P 4e0
P 6h1
h5c1
C
h3
1B1
h5Ph2
1c0
gr v′
Pv
c0d3
0
Pd3
0
P 2c0c0e0
P 3c0e0
P 3j
h3g2
h5h2
1e0
G3gn
e30
c0e0c0e0
d2
0c0d0
d2
0i
Ph3
1u
P 4d0h4
1
P 5h2
1c0
P 6h2
D1
d1g
G3
e0m
τh0e3
0
Ph1v
ik
P 2c0d2
0
P 3d2
0
P 4h2
1e0
i1
h5c0d0
B8
x′
d0u
c0d2
0e0
Pd2
0e0
Pc0d0c0d0
P 2d0c0d0
P 2d0i
P 6h4
1
τG
h5c0d0
h5ih1d1g
R1
e20g
e20h2
1e0
d0e0c0d0
d2
0j
Pu′
P 4c0d0
P 5d0
B6
h1i1
τh2gn
gm
d0τh0g2
h1d0u
il
P 2u
P 2c0d0e0
P 3d0e0
P 3c0c0d0
P 4c0d0
P 4i
B6
τh2d1g
Ph5e0
Q1
gt h2
1B8
τh0gm
d0v
c0d0e2
0
Ph1u′
d4
0
Pc0e0c0d0
P 2e0c0d0
P 2d0j
P 6c0
D4
Q2
h5c0e0
h5j
D11
τe0g2
e0gh2
1e0
e20c0d0
d2
0kPv′
τh0d4
0
Pij
P 4c0e0
P 5e0
P 7h1
D4
h2
3g2
D2
e1g
e0τh0g2
x′h4
1
d0h1v
imPv′
P 2v
Pc0d3
0
P 2d3
0
P 3c0c0e0
P 4c0e0
P 4j
h2
3g2
j1
h3G3
B21
h5Ph2
1e0
c1g2
τh2gm
e0v
c0e3
0
d3
0e0
c0d2
0c0d0
Pd2
0c0d0
Pd2
0i
P 2h3
1u
P 5d0h4
1
P 6h2
1c0
P 7h2
j1
B3
d1h3g
h2
1Q2
B4
τg3
h0g3
e20c0e0
d2
0l d0u
′
d0τh0d2
0e0
P 2h1v
d0i2
P 3c0d2
0
P 4d2
0
P 5h2
1e0
D3
A′
A+A′
B7
X1
nr
c0x′
e0h1v
jm d0u′
Pd0u
Pc0d2
0e0
P 2d2
0e0
P 2c0d0c0d0
P 3d0c0d0
P 3d0i
P 7h4
1
h2
5
H1
h5n
E1C0
RB22
Ph5c0d0
τe0w
Ph1x′
c0e2
0g
d2
0e20
c0d0e0c0d0
Pd0e0c0d0
Pd2
0j P 2u′
τP 2h0d2
0e0
P 2i2
P 5c0d0
P 6d0
h6
X2C′ h3B6
h5d0e0
τh2c1g2
h2g3
h1c0x′
e0gc0e0
d2
0m
e0u′
e0τh0d2
0e0
Ph1d0u
d0ij
P 3u
P 3c0d0e0
P 4d0e0
P 4c0c0d0
A′′
d2
1
h3Q2
q1
B21h4
1
h2gτh0g2
Ukm
e0u′
Pd0v
c0d4
0 P 2h1u′
Pd4
0
P 2c0e0c0d0
P 3e0c0d0
P 3d0j
P 5h1c0d0
P 7c0
h3D4
h3D2
k1
τB23 c0Q2
h2
1B22
h5Pc0e0
Ph5j
R2
τgw
d0e3
0
c0e2
0c0d0
d3
0c0d0
d3
0i
P 2v′
τPh0d4
0
P 2ij
P 5c0e0
P 6e0
P 8h1
r1
τG0
e1h3gc0D4
c0Q2
τB5
D′
2
nm
d0e0me0v
′
e0τh0d0e2
0
x′Ph4
1 Pd0h1v
d0ik P 2v′
P 3v
P 2c0d3
0
P 3d3
0
P 4c0c0e0
P 5c0e0
P 5j
n1
τQ3
h0Q3
h3j1
X3
C′′
C11
B8d0
h3g3τh2
2g3
d0x′ lm e0v′
h2
1U
Pe0v
c0d3
0e0
Pd3
0e0
Pc0d2
0c0d0
P 2d2
0c0d0
P 2d2
0i P 3h3
1u
P 6d0h4
1
P 7h2
1c0
P 8h2
d2 h6h4
1
h1r1
h3(A+A′)
G21 h3B7
h2B23
h3g3τB8d0
G11
e40
c0e2
0c0e0
d2
0e0c0d0
d3
0j
Pd0u′
Pd0τh0d2
0e0
P 3h1v
P 2ik
P 4c0d2
0
P 5d2
0
P 6h2
1e0
p′
h3H1
h2G0
D′
3
h1X3
P (A+A′)
h2B5
τW1
B1c0d0
e20m
e0τh0e3
0
Pc0x′
d0h1d0u
P 2x′
d2
0z Pd0u′
P 2d0u
P 2c0d2
0e0
P 3d2
0e0
P 3c0d0c0d0
P 4d0c0d0
P 4d0i
P 8h4
1
h3h6
p1
h2Q3
d1e1
h2
3B6
B8e0
m2
e0x′
h2
1d0x′
Pc0x′
R′
1 d2
0v
c0d2
0e20
d5
0
Pc0d0e0c0d0
P 2d0e0c0d0
P 2d2
0j
P 3u′
P 6c0d0
P 7d0
10
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 350
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
The E3-page of the motivic Adams spectral sequence for the cofiber of τ
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
h0 h1 h2
h4
1
h3
c0
Ph1
h2
1c0
Ph2
Ph4
1
h2
3
d0
h0h4 h1h4
Pc0
P 2h1
h2h4
c1
Ph2
1c0
P 2h2
τg
h0g
P 2h4
1
c0d0
h4c0
h2g
h2
0i
P 2c0
P 3h1
h2
1h4c0
P 2h2
1c0
P 3h2
h1h3g
d2
0
h1h3g
P 3h4
1
h2
4
r
P 2d0
h3
0h5
n
h1h5
d1
q
P 3c0
p
P 4h1
h2h5
e20
h2
3g
P 3h2
1c0
P 4h2
h4
1h5
t
x
P 4h4
1
h3h5
e1
h0y
h5c0
c1g
u
P 2h2
0i
f1
Ph1h5
τg2
h0g2
P 4c0
h0c2
τh2
0g2
P 5h1
h2
1h5c0
Ph2h5h3h
2
3g
c0e2
0
τh2c1g
h2g2
P 4h2
1c0
P 5h2
g2
τ2h2g2
τh0h2g2
d0r
h2
3h5
h5d0
τw
P 5h4
1
B1
N
u′
P 4d0
h2
1g2
Ph5c0
τh2
2g2
e0r
h4
0Q′
B2
h1h3g2
d0e2
0
P 5c0
h1h5e0
h1h3g2
P 6h1
h5c1
C
h3
1B1
Ph2
1h5c0
gr
h3g2
h2
1h5e0
gn
P 5h2
1c0
P 6h2
d1g
h1G3
τh0e3
0
i1
B8 h1G3
x′
d0u
P 6h4
1
h5c0d0
h5ih1d1g
B6
?
τh2gn
P 4h2
0i
B6
h5c0e0 τh2d1g
Ph5e0
Q1
gt h2
1B8
c0d0e2
0
P 6c0
Q2
h5c0e0
h5j
D11
τe0g2
h2e2
0g
P 7h1
h2
3g2
h0D2
e1g
x′h4
1
h2
3g2
j1
h2
1D4
h3G3
B21
Ph2
1h5e0
c1g2
P 6h2
1c0
P 7h2
j1
B3
h3d1g
h2
1Q2
τg3
h0g3
d0u′
D3
A′
h3
1D4
nr
c0x′
τh2
0g3
P 7h4
1
h2
5
h5n
E1C0
R h1X1
Ph5c0d0
τgv
d2
0e20
τP 2h0d2
0e0
P 2i2
P 6d0
C′ h3B6
h7
0h6
h5d0e0
τh2c1g2
h2g3
h1h6
d2
1
h3Q2
q1
τh0h2g3
h2
1c0x′ + U
km
P 7c0
h2H1
k1
h0h3D2
h2
1X2
c0Q2
h2B22 Ph5c0e0
Ph5j
τgw
P 8h1
h0h2h6
r1
h3e1g
c0Q2
τB5
D′
2
nm
τQ3
h0Q3
h3j1
X3
C′′
C11
B8d0
τh2
2g3
d0x′ lm
d2
0u
P 7h2
1c0
P 8h2
d2 h4
1h6
h1r1
h3(A+A′)
h2
1D4c0
h2B23h3
0G21
τB8d0
h1h3g3
e40
h2
2h6
p′
h3E1 h1X3
P (A+A′)
h2B5
τW1
h1h3g3
P 8h4
1
h3h6
p1
h2Q3
d1e1
h2
3B6
m2
11
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 350
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
The E4-page of the motivic Adams spectral sequence for the cofiber of τ
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
h0 h1 h2
h4
1
h3
c0
Ph1
h2
1c0
Ph2
Ph4
1
h2
3
d0 h3
0h4
h1h4
Pc0
P 2h1
h2h4
c1
Ph2
1c0
P 2h2
τg
h0g
P 2h4
1
c0d0
h4c0
h2g
h2
0i
P 2c0
P 3h1
h2
1h4c0
P 2h2
1c0
P 3h2
h1h3g
P 3h4
1
h2
4
r
P 2d0
n
h7
0h5
h1h5
d1
q
P 3c0
p
P 4h1
h2h5
e20
h2
3g
P 3h2
1c0
P 4h2
h4
1h5
t
x
P 4h4
1
h3h5
h0y
h5c0
h3d1
c1g
u
P 2h2
0i
f1
Ph1h5
τg2
h0g2
P 4c0
h0c2
τh2
0g2
P 5h1
h2
1h5c0
Ph2h5h3h
2
3g
c0e2
0
τh2c1g
h2g2
P 4h2
1c0
P 5h2
g2
τ2h2g2
τh0h2g2
d0r
h2
3h5
h5d0
τw
P 5h4
1
B1
N
u′
h2
1g2
Ph5c0
τh2
2g2
e0r
h7
0Q′
B2
h1h3g2
P 5c0
P 6h1
h5c1
C
Ph2
1h5c0
gr
h3g2
gn
P 5h2
1c0
P 6h2
d1g
h1G3
i1
B8
P 6h4
1
h1d1g
h0h5i
h6
1h5e0
B6
?
P 4h2
0i
τh2d1g
Q1
gt
P 6c0
Q2
D11
h2d0g2
P 7h1
h2
3g2
h0D2
Ph2
1h5e0
h2
3g2
j1
h2
1D4
h3d1gh3G3
B21
c1g2
P 6h2
1c0
P 7h2
j1
B3
h3d1g
h2
1Q2
τg3 + h4
1h5c0e0
h0g3
D3
A′
τh2
0g3
P 7h4
1
h2
5
h5n
E1 + C0
h4
1D4
R
Ph5c0d0
τP 2h0d2
0e0
P 2i2
P 6d0
C′ h3B6
h5d0e0
τh2c1g2
h2g3
h15
0h6
h1h6
d2
1
h3Q2
q1
τh0h2g3
km
P 7c0
h2H1
k1
h0h3D2
h2
1X2
c0Q2
h2B22
Ph5j
τgw + h4
1X1
P 8h1
h0h2h6
r1
h3e1g
c0Q2
τB5
D′
2
τQ3
h0Q3
h3j1
X3
C11
τh2
2g3
d0x′ lm
P 7h2
1c0
P 8h2
d2 h4
1h6
h1r1
h3(A+A′)
h2B23h3
0G21
τB8d0
h1h3g3
h2
2h6
p′
h3(E1 + C0)h1X3
P (A+A′)
τW1
h1h3g3
P 8h4
1
h3h6
p1
h2Q3
d1e1
h3h3B6
h2C′′
m2
12
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 350
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
The E∞-page of the motivic Adams spectral sequence for the cofiber of τ
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
h0 h1 h2
h4
1
h3
c0
Ph1
h2
1c0
Ph2
Ph4
1
h2
3
d0 h3
0h4
h1h4
Pc0
P 2h1
h2h4
c1
Ph2
1c0
P 2h2
τg
h0g
P 2h4
1
c0d0
h4c0
h2g
h2
0i
P 2c0
P 3h1
h2
1h4c0
P 2h2
1c0
P 3h2
h1h3g
P 3h4
1
h2
4
r
n
h10
0h5
h1h5
d1
q
P 3c0
p
P 4h1
h2h5
e20
h2
3g
P 3h2
1c0
P 4h2
h4
1h5
t
x
P 4h4
1
h2
0h3h5
h0y
h1h3h5
h5c0
h3d1
c1g
u
P 2h2
0i
f1
Ph1h5
τg2
h0g2
P 4c0
h0c2
τh2
0g2
P 5h1
h2
1h5c0
Ph2h5h3h2
3g
c0e2
0
τh2c1g
h2g2
P 4h2
1c0
P 5h2
g2
τ2h2g2
τh0h2g2
d0r
h2
3h5
h5d0
τw
P 5h4
1
B1
N
u′
h2
1g2
Ph5c0
τh2
2g2
e0r
h7
0Q′
B2
h1h3g2
P 5c0
P 6h1
h5c1
C
Ph2
1h5c0
gr
h3g2
gn
P 5h2
1c0
P 6h2
d1g
h1G3
i1
B8
P 6h4
1
h1d1g
h0h5i
h6
1h5e0
B6
?
P 4h2
0i
τh2d1g
Q1
gt
P 6c0
Q2
D11
h2d0g2
P 7h1
h2
3g2
h0D2
Ph2
1h5e0
h2
3g2
j1
h2
1D4
h3d1gh3G3
B21
c1g2
P 6h2
1c0
P 7h2
j1
B3
h3d1g
h2
1Q2
τg3 + h4
1h5c0e0
h0g3
D3
A′
τh2
0g3
P 7h4
1
h2
5
h5n
E1 + C0
h4
1D4
R
Ph5c0d0
C′ h3B6
h5d0e0
τh2c1g2
h2g3
h25
0h6
h1h6
d2
1
h3Q2
q1
τh0h2g3
km
P 7c0
h2H1
k1
h0h3D2
h2
1X2
c0Q2
h2B22
Ph5j
τgw + h4
1X1
P 8h1
h0h2h6
r1
h3e1g
c0Q2
τB5
D′
2
τQ3
h0Q3
h3j1
X3
C11
τh2
2g3
d0x′ lm
P 7h2
1c0
P 8h2
d2 h4
1h6
h1r1
h3(A+A′)
h2B23h3
0G21
τB8d0
h1h3g3
h2
2h6
p′
h3(E1 + C0)h1X3
P (A+A′)
τW1
h1h3g3
P 8h4
1
h3h6
p1
h2Q3
d1e1
h3h3B6
h2C′′
m2