Wall-crossing and $p$-adic Artin formalism for ${\mathrm{GSp}}_4\times {\mathrm{GL}}_2\times {\mathrm{GL}}_2$

Abstract

The goal of this article is to develop a $p$-adic Artin formalism in the context of $p$-adic families of automorphic forms on ${\mathrm{GSp}}_4\times {\mathrm{GL}}_2\times {\mathrm{GL}}_2$. Our treatment is guided by the (double) wall-crossing principle, emphasising an interplay between arithmetic GGP and $p$-adic explicit GGP formulae. Although the picture we present remains largely conjectural, we provide evidence in favour of our conjectures (a) in terms of algebraic $p$-adic $L$-functions, and (b) in endoscopic scenarios.

45 pages, comments most welcome!