What is a Shimura Variety?
نویسنده
چکیده
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.
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When Weil arrived in Tokyo in 1955, planning to speak about his ideas on the extension to abelian varieties of the classical theory of complex multiplication, he was surprised to learn that two young Japanese mathematicians had also made decisive progress on this topic. They were Shimura and Taniyama. While Weil wrote nothing on complex multiplication except for the report on his talk, Shimura ...
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