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Overconvergence of étale $(\varphi,\Gamma)$-modules in families

Part of: Discontinuous groups and automorphic forms Algebraic number theory: local and $p$-adic fields

Published online by Cambridge University Press:  10 July 2025

Gal Porat
Gal Porat*
Affiliation:
The Hebrew University, Jerusalem, 9190401, Israel galporat1@gmail.com
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Abstract

We prove a conjecture of Emerton, Gee and Hellmann concerning the overconvergence of étale $(\varphi,\Gamma)$-modules in families parametrized by topologically finite-type $\mathbf{Z}_{p}$-algebras. As a consequence, we deduce the existence of a natural map from the rigid fiber of the Emerton–Gee stack to the rigid analytic stack of $(\varphi,\Gamma)$-modules.

Keywords

p-adic Hodge theoryp-adic Galois representations

MSC classification

Primary: 11F80: Galois representations
Secondary: 11S25: Galois cohomology

Information

Type
Research Article
Information
Compositio Mathematica , Volume 161 , Issue 3 , March 2025 , pp. 555 - 593
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Copyright
© The Author(s), 2025. The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence.

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