Wall-crossing and p-adic Artin formalism for \rm GSp₄ × \rm GL₂ × \rm GL₂

2025/09/25 by Kâzım Büyükboduk, Büyükboduk, Kâzım, Óscar Rivero +3
Mathematics · #11F85 #14G35 #1R23 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2509.20887

openalex publication_date 2025/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \rm GSp₄ × \rm GL₂ × \rm GL₂. 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.

Citations

• On the Artin formalism for triple product p-adic L-functions
• On the Artin formalism for triple product p-adic L-functions: Chow--Heegner points vs. Heegner points
• On the Bernstein-Zelevinsky classification and epsilon factors in families
• Higher Coleman Theory
• Perfectoid overconvergent Siegel modular forms and the overconvergent Eichler-Shimura morphism
• Hida families and p-adic triple product L-functions
• On Selmer groups and factoring p-adic L-functions
• P-Adic families of Siegel modular cuspforms
• Several variable p-adic families of Siegel-Hilbert cusp eigensystems and their Galois representations

Related

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• p-adic L-functions for \rm GSp(4)×\rm GL(2)
• Towards the wall-crossing of locally ℚ_p-analytic representations of GL_n(K) for a p-adic field K
• p-adic L-functions for \rm GSp(4)× \rm GL(2) II
• Nearly higher Coleman theory and p-adic L-functions for GSp(4) × GL(2) and GSp(4) × GL(2) × GL(2)