Isogeny decompositions and the Tate--Shafarevich group modulo squares

Abstract: We present a method for decomposing abelian varieties up to isogeny using group actions and finite group representation theory. As an application, we show that given a square-free natural number n, there exists an abelian variety with finite Tate--Shafarevich group of order n times a square.

number theory

Audience: researchers in the topic

London number theory seminar

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