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).
An online bookstore
In May 2016, PUP will be publishing a paperback edition. Alas, they refused to allow me to add a short addendum/erratum.
Sales as of June 30, 2015: 4088. Papers citing the
book since 1997 or 2000(MR): 832. Total citations (GScholar): 2507 .
|Notes for a revised expanded version.
|1. Etale Morphisms||16.11.14|
|2. Sheaf Theory||NA|
|4. The Brauer Group||23.11.15|
|5. The Cohomology of Curves and Surfaces||NA|
|6. The Fundamental Theorems||NA|
|B. Spectral Sequences||NA|
|D. Derived Categories||07.09.13||
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)
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.
- Unipotent automorphic representations: global motivation, James Arthur.
- Motifs et formes automorphes: applications du principe de functorialité, Laurent Clozel.
- Shimura varieties and λ-adic representations, Robert E. Kottwitz.
- The present state of the trace formula, J.-P. Labesse.
- Faisceaux automorphes lié aux séries d'Eisenstein, G. Laumon.
- Canonical models of (mixed) Shimura varieties and automorphic vector bundles, J.S. Milne.
- Automorphic L-functions, F. Shahidi.
- Automorphic forms and Galois representations: some examples, Don Blasius.
- Non-abelian Lubin-Tate theory, H. Carayol.
- Automorphic forms and the cohomology of vector bundles on Shimura varieties, Michael Harris.
- p-adic L-functions for base change lifts of
GL2 to GL3, Haruzo Hida.
- Exterior square L-functions, Hervé Jacquet and Joseph Shalika.
- Problems arising from the Tate and Beilinson conjectures in the context of Shimura varieties, Dinakar Ramakrishnan.
- On the bad reduction of Shimura varieties, M. Rapoport.
- Representations of Galois groups associated to Hilbert modular forms, Richard Taylor.
- The Lefschetz trace formula for an open algebraic surface, Thomas Zink.
- L2-cohomology of Shimura varieties, Steven Zucker.
Posted with the permission
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
Comments on Print on Demand publishing