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Preprints, Working Papers, ... Year : 2024

Patching and multiplicities of p-adic eigenforms

Abstract

We prove the existence of non-classical $p$-adic automorphic eigenforms associated to a classical system of eigenvalues on definite unitary groups in $3$ variables. These eigenforms are associated to Galois representations which are crystalline but very critical at $p$. We use patching techniques related to the trianguline variety of local Galois representations and its local model. The new input is a comparison of the coherent sheaves appearing in the patching process with coherent sheaves on the Grothendieck--Springer version of the Steinberg variety given by a functor constructed by Bezrukavnikov.
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hal-04607508 , version 1 (10-06-2024)

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Eugen Hellmann, Valentin Hernandez, Benjamin Schraen. Patching and multiplicities of p-adic eigenforms. 2024. ⟨hal-04607508⟩
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