The Bloch—Kato conjecture for GSp(4)

Abstract: In my talk, I will sketch a proof of new cases of the Bloch—Kato conjecture for the spin Galois representation attached to genus 2 Siegel modular forms. More precisely, I will show that if the L-function is non-vanishing at some critical value, then the corresponding Selmer group is zero, assuming a number of technical hypotheses. I will also mention work in progress on extending this result to Siegel modular forms of parallel weight 2, with potential applications to the Birch—Swinnerton-Dyer conjecture for abelian surfaces. This is joint work with David Loeffler.

algebraic geometrynumber theoryrepresentation theory

Audience: researchers in the topic

Columbia Automorphic Forms and Arithmetic Seminar