p-adic rigidity for GSp₄

2026/07/31 by Charlotte Clare-Hunt
Mathematics · #math.NT #msc:11F80 #msc:11F46 #msc:11F67

paper · pdf

25 pages; minor revisions

arxiv created 2026/08/06 · arxiv updated 2026/08/07

Abstract

This paper establishes the p-adic rigidity of certain suitably refined noncuspidal automorphic Saito\unicodex2013Kurokawa representations of GSp₄(\mathbbA_ℚ), in the sense that they cannot be interpolated in a nontrivial positive dimensional p-adic family. The results provide a GSp₄ analogue of Bellaïche's rigidity theorems for U(2,1) and identify an obstruction to p-adic variation on the GSp₄ eigenvariety.

Citations

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• The Local Langlands Conjecture for GSp(4)
• The local Langlands conjecture for GSp(4)
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• On the semi-simplicity of the U_p-operator on modular forms
• Galois representations associated to Siegel modular forms of low weight
• Class fields of abelian extensions of Q