$p$-adic rigidity for $\mathrm{GSp}_4$

Charlotte Clare-Hunt

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arXiv · 2607.02815

$p$-adic rigidity for $\mathrm{GSp}_4$

Charlotte Clare-Hunt

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Abstract

This paper establishes the $p$-adic rigidity of certain suitably refined noncuspidal automorphic Saito$\unicode{x2013}$Kurokawa representations of $\mathrm{GSp}_4(\mathbb{A}_\mathbb{Q})$, in the sense that they cannot be interpolated in a nontrivial positive dimensional $p$-adic family. The results provide a $\mathrm{GSp}_4$ analogue of Bella\"{i}che's rigidity theorems for $\mathrm{U}(2,1)$ and identify an obstruction to $p$-adic variation on the $\mathrm{GSp}_4$ eigenvariety.

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Charlotte Clare-Hunt. 2026-07-02. $p$-adic rigidity for $\mathrm{GSp}_4$. https://arxiv.org/abs/2607.02815

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