FORMAL GROUPS AND APPLICATIONS

MICHIEL HAZEWINKEL

AMS CHELSEA PUBLISHING !"#$%&'("&)&

FORMAL GROUPS AND APPLICATIONS

FORMAL GROUPS AND APPLICATIONS

MICHIEL HAZEWINKEL

AMS CHELSEA PUBLISHINGAmerican Mathematical Society • Providence, Rhode Island

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http://dx.doi.org/10.1090/chel/375.H

2010 Mathematics Subject Classification. Primary 14L05; Secondary 16Txx, 05Exx,11Fxx, 11Sxx, 12Fxx, 13F35, 55N22.

For additional information and updates on this book, visitwww.ams.org/bookpages/chel-375

Library of Congress Cataloging-in-Publication Data

Hazewinkel, Michiel.Formal groups and applications / Michiel Hazewinkel.

pages cmIncludes bibliographical references and index.ISBN 978-0-8218-5349-8 (alk. paper)1. Formal groups. I. Title.

QA177.4.H39 2012512′.2—dc23

2012028054

Copying and reprinting. Individual readers of this publication, and nonprofit librariesacting for them, are permitted to make fair use of the material, such as to copy a chapter for usein teaching or research. Permission is granted to quote brief passages from this publication inreviews, provided the customary acknowledgment of the source is given.

Republication, systematic copying, or multiple reproduction of any material in this publicationis permitted only under license from the American Mathematical Society. Requests for suchpermission should be addressed to the Acquisitions Department, American Mathematical Society,201 Charles Street, Providence, Rhode Island 02904-2294 USA. Requests can also be made bye-mail to reprint-permission@ams.org.

c© 1978 held by the author. All rights reserved.Reprinted with corrections by the American Mathematical Society, 2012.

Printed in the United States of America.

©∞ The paper used in this book is acid-free and falls within the guidelinesestablished to ensure permanence and durability.

Visit the AMS home page at http://www.ams.org/

10 9 8 7 6 5 4 3 2 1 17 16 15 14 13 12

Preface to the Corrected Printing xiPreface xiiiLeitfaden and Indicien xvIntroduction xix

Preface to the corrected printing

Some two years ago the idea arose for a second (corrected) printing of my bookFormal Groups and Applications, Academic Press, 1978. The initiative originatedwith the American Mathematical Society in the person of Sergei Gelfand.

Naturally the plan was to include an update chapter, outlining what had hap-pened since 1978. I readily agreed to that, thinking that not all that much hadhappened (except as regards interrelations of formal groups with algebraic topol-ogy) and that some 100 pages would suffice for an update chapter.

I was vastly mistaken in my estimates. Meanwhile, I have collected well over2400 relevant papers in published or preprint form and to do even marginal justiceto all this material requires a second volume of Formal Groups and Applicationscomparable in size to the first one. That second volume, also to be published by theAmerican Mathematical Society, is now in the process of being written. Currentlyit looks like the manuscript will be ready in the spring of 2013.

Meanwhile, here is a corrected printing of the original volume from 1978, com-plete with some three pages worth of corrections and a few short addenda. Noneof the corrections is very serious and all of the misprints involved can easily becorrected by the (attentive) reader. Still it is probably worthwhile having themlisted.

There is little hope that I have really caught all misprints; so I will be gratefulfor the signaling of additional misprints on the part of generous readers.

The original edition of Formal Groups and Applications has been out of print formany years now and seems to be not always easy to get hold of even via universitylibraries. So I hope and trust that this corrected printing will be useful.

Michiel HazewinkelBussum, 18 June 2012

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theorie des groupes algebriques, CBRM (1962), 77–86. (E.4.1)

M. I. Basmakov

M. I. Basmakov

M. I. Basmakov

M. I. Basmakov

ˇA. S. Kuroskin,

ˇA. S. Kuroskin,

P. Berthelot, Slopes of Frobenius in cristalline cohomology, in R. Hartshorne (ed.), Algebraicgeometry, Proc. Symp. Pure Math. 29 (1975), 315–328. (B.2.3)P. Berthelot, Cohomology cristalline des schemas de caracteristique p > 0, LNM 407 (1974).(B.2.3, 38.2.2)

E. J. Ditters, Groupes formels, Cours 3e cycle 73/74, Univ. Paris, 11th, Orsay, 108p. (1975).(E.5.5, E.5.1, 38.4.7, E.4.3, 38.4.5)

J. M. Fontaine, Points d’ordre fini d’un groupe formel sur une extension non-ramifie de Zp,Journees Arithmetiques Grenoble, Bull. Soc. Math. France mem. 37 (1973), 75–79. (E.5.4)

A. Grothendieck, Categories fibres et descente, Sem. Geomet. Algeb. 1 (1960/1961), exposeVI. (E.3.1)

M. Hazewinkel, Une theorie de Cartier-Dieudonne pour les A-modules formels, C.R. Acad.Sci. Paris 284 (1977), 655–657. (E.4.5)

N. Jacobson, “Lectures in Abstract Algebra,” 3 vols, van Nostrand-Reinhold, Princeton,New Jersey, 1951, 1953, 1964. (35.2.8, 24.1.3)

N. Jacobson, The theory of rings, Math. Surveys 2, AMS, 1943. (35.5.9, E.4.4, 28.4.5)

M. Karoubi, Cobordisme et groupes formels, Sem. Bourbaki 1971/72, Expose 408, LectureNotes Math. Vol. 317. Springer-Verlag, Berlin and New York, 1973.

N. Roby, Lois polynomes et lois formelles en theorie des modules, Ann. Ecole Norm. Sup. 80(1963), 213–348.

38.2.8, T38.2.11

λ-ring, E.2.1, 17.2universal, on one generator, E.6.3

Landweber-Novikov operators, 31.1.8Lazard comparison lemma,

see comparison lemmaLazard ring, 1.5.3Lie algebra

of a formal group (law) D9.7, D14.1,D37.5.13, T14.2.3

free, D14.4.7, T14.4.9Lie morphism, 14.3Lie theory, formal, 14.2.3, 37.4Lie’s third theorem, formal version, 14.5, 37.4.11Lifting (a formal group law), 18.5.14Local-global theorems (for formal group laws),

20.5LogarithmA, of a formal A module, 21.5.7, 25.4.6of a formal group law, 5.4of the formal group law of complex cobord-

ism, T31.1.7, T34.2.14relation with log (1 + z), 36.3.1, 38.3.3

Lubin-Tate formal group law (formal A-module)

adjointness theorem, T30.2.9, T30.2.10as functional equation formal group laws,

8.3.6, 13.4generalized, E9.7, D13.2.1, D30.1.8more dimensional, 13.3

CHEL/375.H