|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|
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
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.
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