Troletti, Daniele (2019) Abelian variety with Tate-Shafarevich group of non-square order. [Magistrali biennali]
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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.
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