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

Kâzım Büyükboduk; Óscar Rivero; Ryotaro Sakamoto

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arXiv · 2509.20887

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

Kâzım Büyükboduk·Óscar Rivero·Ryotaro Sakamoto

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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 ${\rm GSp}_4 \times {\rm GL}_2 \times {\rm GL}_2$. 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.

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Kâzım Büyükboduk, Óscar Rivero, Ryotaro Sakamoto. 2025-09-25. Wall-crossing and $p$-adic Artin formalism for ${\rm GSp}_4 \times {\rm GL}_2 \times {\rm GL}_2$. https://arxiv.org/abs/2509.20887

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