pdf file for my manuscript (30.04.11, 76 pages).
pdf file for published version (15.10.12, 82 pages).
Caution: the numbering differs (see below).
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.
As much as possible, I have included complete proofs.
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.
Published version
The article was published in
Handbook of Moduli (Gavril Farkas, Ian Morrison, Editors),
International Press of Boston, 2013, Vol II, 462--544.
In the published version, equations and theorem-like statements are numbered in sequence.
For example, equation (10), p25, has become (6.2) (first equation after 6.1), and
Proposition 6.2 has become 6.3 (third numbered equation or theorem-like statement in section 6).
Notes
There is some overlap between this article and the book,
Mumford-Tate Groups and Domains by Green, Griffiths, and Kerr 2012.
In particular, their notion of a
"Mumford-Tate domain'' (ibid. p.52) is the special
case of our "period subdomain" in which the family of Hodge tensors
contains all such tensors, except that, whereas our subdomain
is a (connected)
orbit under $G(\mathbb{R})^+$, their domain is an orbit under
$G(\mathbb{R})$.
Corrections
6.23 Should read: Let (V,F) be a family (not variation).
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. Posted it as arXiv:1105.0887.