Philadelphia Area Number Theory Seminar

Wednesday, April 12, 2023 - 2:30pm

Sam Mundy

Princeton University

Given an automorphic representation π of SO(n, n + 1) with certain nice properties at infinity, one can nowadays attach to π a p-adic Galois representation R of dimension 2n. The Bloch–Kato conjectures then predict in particular that if the L-function of R vanishes at its central value, then the Selmer group attached to a particular twist of R is nontrivial. I will explain work in progress proving the nonvanishing of these Selmer groups for such representations R, assuming the L-function of R vanishes to odd order at its central value. The proof constructs a nontrivial Selmer class using p-adic deformations of Eisenstein series attached to π, and I will highlight the key new input coming from local representation theory which allows us to check the Selmer conditions for this class at primes for which π is ramified.