P-adic L-functions and diagonal cycles for GSp(4) x GL(2) x GL(2)

TL;DR

This paper develops a conjectural framework for p-adic L-functions associated with automorphic forms on GSp(4) x GL(2) x GL(2), linking them to Galois cohomology and algebraic cycles, extending prior diagonal cycle theories.

Contribution

It generalizes the theory of diagonal cycles to the GSp(4) x GL(2) x GL(2) setting and proposes a conjectural p-adic L-function interpolation framework.

Findings

Proposes a conjectural theory of p-adic L-functions for GSp(4) x GL(2) x GL(2)

Links p-adic L-functions to Galois cohomology classes and algebraic cycles

Extends the diagonal cycle framework to a new automorphic setting

Abstract

We develop a (largely conjectural) theory of p-adic L-functions interpolating square roots of central L-values for automorphic forms on GSp(4) x GL(2) x GL(2), and a relation between these p-adic L-functions and families of Galois cohomology classes interpolating algebraic cycles. Our theory is a generalisation of the theory of "diagonal cycles" developed by Darmon and Rotger for the GL(2) triple product.