The University of Sydney
School of Mathematics and Statistics  
Number Theory Seminar  

University of Sydney Number Theory Seminar

Steve Ward

Thursday 8 June, 4:05-5:30PM, Carslaw 375

The Main Theorem of Complex Multiplication for Abelian Varieties

This week I will sketch a proof of the Main Theorem of Complex Multiplication, as presented in Shimura's book. The talk will be slightly longer than one hour, and will be divided into two halves. In the first, I will collect facts about polarised abelian varieties of a given type, and reduction modulo a prime. In the second half, I will use the assembled theory, as well as the tools from class field theory I discussed last week to prove the Main Theorem.