What is a Shimura Variety? J.S. Milne   Top
Expository Notes
A Primer of Commutative Algebra
Motives---Grothendieck's Dream
What is a Shimura Variety?
Introduction to Shimura Varieties
Shimura Varieties and Moduli
Tannakian Categories
The Work of Tate

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Most mathematicians have encountered modular functions. For example, when the group theorists discovered the monster group, they were surprised to find that the degrees of its irreducible representations were already encoded in the q-coefficients of the j-function. The theory of Shimura varieties grew out of the applications of modular functions and modular forms to number theory. Roughly speaking, Shimura varieties are the varieties on which modular functions live.


Notices of the AMS, December 2012.


Posted May 13, 2012 (3 pages).
Minor revision September 1, 2012.