pdf (current version 30.04.11, 76 pages).
Abstract
Connected Shimura varieties are the quotients of hermitian symmetric domains
by discrete groups defined by congruence conditions. We examine their relation with moduli varieties.
Contents
Elliptic modular curves;
hermitian symmetric domains;
discrete subgroups of Lie groups;
locally symmetric varieties;
variations of Hodge structures;
Mumford-Tate groups and their variation in families;
Period subdomains;
variations of Hodge structures on locally symmetric varieties;
absolute Hodge classes and motives;
symplectic representations;
moduli.
About
This article will appear in Handbook of Moduli (Gavril Farkas, Ian Morrison, Editors).
As much as possible, I have included complete proofs.
History
v1.00 (December 1, 2010) First version on the web. 69 pages.
pdf
v2.00 (April 30, 2011). Improvements to the exposition. some misprints fixed.