Every abelian variety has an associated Tate-Shafarevich group defined using cohomology. Cassels and Tate proved the existence of a pairing on this group. This pairing forces the order of the Tate-Shafarevich group to be a square in the case of the elliptic curves. This is no longer true in higher dimension. In this thesis we try to develop new examples of this failure to be a square using modular curves.

Abelian variety with Tate-Shafarevich group of non-square order

Troletti, Daniele
2019/2020

Abstract

Every abelian variety has an associated Tate-Shafarevich group defined using cohomology. Cassels and Tate proved the existence of a pairing on this group. This pairing forces the order of the Tate-Shafarevich group to be a square in the case of the elliptic curves. This is no longer true in higher dimension. In this thesis we try to develop new examples of this failure to be a square using modular curves.
2019-07-05
56
Abelian variety, Tate-Shafarevich group
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12608/28023