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

数学学院

Tata Institute of Fundamental Research
Eötvös Loránd University
MTA Lendület Automorphic Research Group

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

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.

源语言	英语
页（从-至）	521-546
页数	26
期刊	Bulletin de la Societe Mathematique de France
卷	149
期	3
DOI	https://doi.org/10.24033/bsmf.2837
出版状态	已出版 - 2023

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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.",

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AU - Wei, Feng

AU - Zábrádi, Gergely

PY - 2023

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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.

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KW - p-adic Galois representations

KW - Étales (φ, Γ)-module

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

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