Harmonic Analysis, the Trace Formula, and Shimura Varieties: Proceedings of the Clay Mathematics Institute, 2003 Summer School, the Fields Institute, ... 2-27, 2003

by James Arthur (Editor)

In these proceedings from the school held in June 2003, the presenters give introductions to the subject of automorphic forms that have come to be called the Langlands program. Although the reciprocity laws proposed by Langlands are still largely unproved, the program ties arithmetic information from number theory and algebraic geometry with analytic information from harmonic analysis and group representation. The presenters' topics include an introduction to the trace formula and Shimura varieties (including those with bad reductions of parahoric type), linear algebraic groups, harmonic analysis on reductive p-adic groups and Lie algebras, homogeneity for reductive p-adic groups, compactifications and cohomology of modular varieties, the fundamental lemma, and the generalized Ramanujan conjectures. Annotation ©2006 Book News, Inc., Portland, OR (booknews.com)

689 pages, Paperback

First published January 1, 2005

Reviews

[Andrew]

I wish I had read Milne's notes on Shimura varieties sooner.

In general, these articles have a friendly exposition.