Edwina Aylward

Parity results for abelian varieties over global function fields

This talk will focus on abelian varieties over global function fields. I will begin with their L-functions, the Birch–Swinnerton-Dyer conjecture, and the parity conjecture. In this setting much more is known than over number fields, and I will highlight the key reasons for this. In particular, the p-parity conjecture is a theorem over global function fields, in contrast to the number field case. I will describe the tools and ideas that make the proof possible, and explain how the same methods can be extended to obtain p-parity results for twists by orthogonal Artin representations.