Published Books - J.S. Milne, Top
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Year Title pdf Erratum
1980 Etale Cohomology none notes
1982 Hodge Cycles, Motives, and Shimura Varieties (with Deligne, Ogus, Shih) DMOS notes
1986 Arithmetic Duality Theorems ADT1 notes
2006 Arithmetic Duality Theorems, second edition ADT2 notes
1990 Automorphic Forms, Shimura Varieties, and L-functions, (editor with L. Clozel) Vol. 1 none
    Proc. of a Conf. held at the Univ. of Michigan, Ann Arbor, July 6--16, 1988. Vol. 2 none
2006 Elliptic Curves EC Erratum
2017 Algebraic Groups: the theory of group schemes of finite type over a field. CUP Erratum

1980 Etale Cohomology

Princeton Mathematical Series 33, Princeton University Press, 323+xiii pages, ISBN 0-691-08238-3
An exposition of étale cohomology assuming only a knowledge of basic scheme theory.
In print. List price 150 USD (1980 price was $26.50=$76.50 in 2015 dollars). PUP, An online bookstore, Review
In February 2017, PUP will be publishing a paperback edition. Alas, they refused to allow me to add a short addendum/erratum.
Sales as of June 30, 2017: 4116. Papers citing the book since about 2000(MR): 938. Citations (GScholar): 2804.

Notes for a revised expanded version.  
1. Etale Morphisms16.11.14
2. Sheaf TheoryNA
3. CohomologyNA
4. The Brauer Group23.11.15
5. The Cohomology of Curves and SurfacesNA
6. The Fundamental TheoremsNA
A. LimitsNA
B. Spectral SequencesNA
C. HypercohomologyNA
D. Derived Categories07.09.13
In the 1970s, derived categories were still quite new, and known to only a few algebraic geometers, and so I avoided using them. In some places this worked out quite well, for example, contrary to statements in the literature they are not really needed for the Lefschetz trace formula with coefficients in Z/mZ, but in others it led to complications. Anyone who doubts the need for derived categories should try studying the Kunneth formula (VI, 8) without them. In the new version, I shall use them.

I also regret treating Lefschetz pencils only in the case of fiber dimension 1. Apart from using derived categories and including Lefschetz pencils with arbitrary fiber dimension, I plan to keep the book much as before, but with the statements of the main theorems updated to take account of later work. Whether the new version will ever be completed, only time will tell.

1982 Hodge Cycles, Motives, and Shimura Varieties (with Pierre Deligne, Arthur Ogus, Kuang-yen Shih)

Lecture Notes in Math. 900, Springer-Verlag, 1982, 414 pages, ISBN 3-540-11174-3 and 0-387-11174-3
Usually out of print. List price 99.00 USD (paperback) Springer Available online at springerlink for 29.95 USD per section.

1986 Arithmetic Duality Theorems

Academic Press, 421+x pages, ISBN 0-12-498040-6. Out of print.
Proves the duality theorems in Galois, étale, and flat cohomology that have come to play an increasingly important role in number theory and arithmetic geometry,
2006 Second corrected TeXed edition (paperback).
Booksurge Publishing, 339+viii pages, ISBN 1-4196-4274-X
Available from bookstores worldwide. List price 24 USD. An online bookstore
The posted version (click 2006) agrees with published version except for the copyright page (for more information, see adt.html).

1990 Automorphic Forms, Shimura Varieties, and L-functions, (editor with L. Clozel)

Proceedings of a Conference held at the University of Michigan, Ann Arbor, July 6--16, 1988.

Volume I

Volume II

Posted with the permission of Elsevier.
How I scanned these (since people keep asking). Comments on Copyright and Fair Use Law.

2006 Elliptic Curves

Booksurge Publishing, 246 pages, ISBN 1-4196-5257-5 (ISBN is for the softcover version).
This book uses the beautiful theory of elliptic curves to introduce the reader to some of the deeper aspects of number theory.
Softcover version available from bookstores worldwide. List price 17 USD; an online bookstore.
Library of Congress Number (LCCN): 2006909782 (full data in process).
Some corrections doc

Following is the blurb for Elliptic Curves that was on Amazon, and would still be, but for the incompetence of the people at BookSurge/CreateSpace/Amazon.

This book uses the beautiful theory of elliptic curves to introduce the reader to some of the deeper aspects of number theory. It assumes only a knowledge of the basic algebra, complex analysis, and topology usually taught in advanced undergraduate or first-year graduate courses.

Indeed, the book is affordable (in fact, the most affordable of all references on the subject), but also a high quality work and a complete introduction to the rich theory of the arithmetic of elliptic curves, with numerous examples and exercises for the reader, many interesting remarks and an updated bibliography.
Mathematical Reviews, Álvaro Lozano-Robledo

J. S. Milne's lecture notes on elliptic curves are already well-known … The book under review is a rewritten version of just these famous lecture notes from 1996, which appear here as a compact and inexpensive paperback that is now available worldwide.
Zentralblatt MATH, Werner Kleinert

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