pdf (current version 1.00).
Abstract
Shimura varieties are initially defined as complex manifolds
(quotients of Hermitian symmetric domains by congruence
groups), but is known that they are algebraic varieties
defined in a natural way over number fields. The oldest
examples are the elliptic modular curves (quotients of the
complex upper half plane by congruence subgroups of SL(2,Z).
In the talk, I'll explain these two sentences, and also why
Langlands was so interested in Shimura varieties.
About
These are my notes for a "popular" talk in the `What is ...?'
seminar at the University of Michigan, November 17, 2010.
History
v1.00 (November 18, 2009). First version on the web (11 pages).