P-adic interpolation of Gross--Prasad periods and diagonal cycles

David Loeffler (Warwick)

30-Oct-2020, 14:30-16:00 (3 years ago)

Abstract: The Gross--Prasad conjecture for orthogonal groups relates special values of L-functions for SO(n) x SO(n+1) to period integrals of automorphic forms. This conjecture is known for n = 3, in which case the group SO(3) x SO(4) is essentially GL2 x GL2 x GL2; and the study of these GL2 triple product periods, and in particular their variation in p-adic families, has had important arithmetic applications, such as the work of Darmon and Rotger on the equivariant BSD conjecture for elliptic curves.

I'll report on work in progress with Sarah Zerbes studying these periods in the n = 4 case, where the group concerned is isogenous to GSp4 x GL2 x GL2. I'll explain a construction of p-adic L-functions interpolating the Gross--Prasad periods in Hida families, and an 'explicit reciprocity law' relating these p-adic L-functions to diagonal cycle classes in etale cohomology. These constructions are closely analogous to the Euler system for GSp(4) described in Sarah's talk, but with cusp forms in place of the GL2 Eisenstein series.

algebraic geometrynumber theoryrepresentation theory

Audience: researchers in the topic


Columbia Automorphic Forms and Arithmetic Seminar

Organizers: Chao Li*, Eric Urban
*contact for this listing

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