On the local converse theorem and the descent theorem in families

Baiying Liu; Gilbert Moss

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arXiv · 1711.11159

On the local converse theorem and the descent theorem in families

Baiying Liu·Gilbert Moss

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Abstract

We prove an analogue of Jacquet's conjecture on the local converse theorem for \ell-adic families of co-Whittaker representations of GL_n(F), where F is a finite extension of Q_p and \ell does not equal p. We also prove an analogue of Jacquet's conjecture for a descent theorem, which asks for the smallest collection of gamma factors determining the subring of definition of an \ell-adic family. These two theorems are closely related to the local Langlands correspondence in \ell-adic families.

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Baiying Liu, Gilbert Moss. 2017-11-29. On the local converse theorem and the descent theorem in families. https://arxiv.org/abs/1711.11159

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