Abstract

We prove the existence of nonclassical $p$-adic automorphic eigenforms associated to a classical system of eigenvalues on definite unitary groups in three 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. Our input consists of 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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