University of Arizona
When
2 – 3 p.m., Sept. 15, 2026
Where
Title: Galois Deformations and Rank-Zero BSD for Abelian Surfaces
Abstract: The Birch--Swinnerton-Dyer conjecture predicts a deep relation between an abelian variety and its 𝐿-function. Loeffler and Zerbes proved a rank-zero result for modular abelian surfaces, conditional on a deformability hypothesis for the associated automorphic representation. I will explain how this condition can be studied through Galois deformation theory and Selmer groups, and how we verify it for an explicit abelian surface at 𝑝 =3, giving the first example where the hypothesis is proved rather than assumed. This is ongoing joint work with Shiva Chidambaram and Timo Keller.