MULTIVARIABLE (φ, Γ)-MODULES AND REPRESENTATIONS OF PRODUCTS OF GALOIS GROUPS: THE CASE OF THE IMPERFECT RESIDUE FIELD

Jishnu Ray; Feng Wei; Gergely Zábrádi

doi:10.24033/bsmf.2837

MULTIVARIABLE (φ, Γ)-MODULES AND REPRESENTATIONS OF PRODUCTS OF GALOIS GROUPS: THE CASE OF THE IMPERFECT RESIDUE FIELD

Jishnu Ray
, Feng Wei
, Gergely Zábrádi

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

Let K be a complete discretely valued field with mixed characteristic (0, p) and imperfect residue field kα. Let Δ be a finite set. We construct an equivalence of categories between finite dimensional Fp-representations of the product of Δ copies of the absolute Galois group of K and multivariable étale (φ, Γ)-modules over a multivariable Laurent series ring over kα.

Original language	English
Pages (from-to)	521-546
Number of pages	26
Journal	Bulletin de la Societe Mathematique de France
Volume	149
Issue number	3
DOIs	https://doi.org/10.24033/bsmf.2837
Publication status	Published - 2023

Keywords

imperfect residue field
p-adic Galois representations
Étales (φ, Γ)-module

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10.24033/bsmf.2837

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abstract = "Let K be a complete discretely valued field with mixed characteristic (0, p) and imperfect residue field kα. Let Δ be a finite set. We construct an equivalence of categories between finite dimensional Fp-representations of the product of Δ copies of the absolute Galois group of K and multivariable {\'e}tale (φ, Γ)-modules over a multivariable Laurent series ring over kα.",

keywords = "imperfect residue field, p-adic Galois representations, {\'E}tales (φ, Γ)-module",

author = "Jishnu Ray and Feng Wei and Gergely Z{\'a}br{\'a}di",

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AU - Wei, Feng

AU - Zábrádi, Gergely

PY - 2023

Y1 - 2023

N2 - Let K be a complete discretely valued field with mixed characteristic (0, p) and imperfect residue field kα. Let Δ be a finite set. We construct an equivalence of categories between finite dimensional Fp-representations of the product of Δ copies of the absolute Galois group of K and multivariable étale (φ, Γ)-modules over a multivariable Laurent series ring over kα.

AB - Let K be a complete discretely valued field with mixed characteristic (0, p) and imperfect residue field kα. Let Δ be a finite set. We construct an equivalence of categories between finite dimensional Fp-representations of the product of Δ copies of the absolute Galois group of K and multivariable étale (φ, Γ)-modules over a multivariable Laurent series ring over kα.

KW - imperfect residue field

KW - p-adic Galois representations

KW - Étales (φ, Γ)-module

UR - https://www.scopus.com/pages/publications/85173230158

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DO - 10.24033/bsmf.2837

M3 - Article

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ER -

MULTIVARIABLE (φ, Γ)-MODULES AND REPRESENTATIONS OF PRODUCTS OF GALOIS GROUPS: THE CASE OF THE IMPERFECT RESIDUE FIELD

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Keywords

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