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Multivariable $(\varphi ,\Gamma )$-modules and Representations of Products of Galois Groups: The Case of Imperfect Residue Field

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Jishnu Ray, Feng Wei, Gergely Zábrádi

Number Theory · Submitted 25 May 2020

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We construct an equivalence of categories between finite dimensional $\Bbb{F}_p$-representations of the product of $\Delta$ copies of the absolute Galois group of $K$ and multivariable \' etale $(\varphi, \Gamma)$-modules over a multivariable Laurent series ring over $k_K$.

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arXiv ID2005.11887 (version 2)
Pith IDBBHHN5Y3, Pith's permanent record of this paper and its review
CitationFeng Wei, Gergely Z\'abr\'adi, Jishnu Ray. "Multivariable $(\varphi ,\Gamma )$-modules and Representations of Products of Galois Groups: The Case of Imperfect Residue Field." arXiv:2005.11887 (2020). https://pith.science/paper/BBHHN5Y3
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,009 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.19 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.05 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

Let $K$ be a complete discretely valued field with mixed characteristic $(0, p)$ and imperfect residue field $k_K$. Let $\Delta$ be a finite set. We construct an equivalence of categories between finite dimensional $\Bbb{F}_p$-representations of the product of $\Delta$ copies of the absolute Galois group of $K$ and multivariable \' etale $(\varphi, \Gamma)$-modules over a multivariable Laurent series ring over $k_K$.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 Let $K$ be a complete discretely valued field with mixed characteristic $(0, p)$ and imperfect residue field $k_K$. background 1.00 0.07 0.02 asserted 0.87
s1 Let $\Delta$ be a finite set. background 0.99 0.08 0.01 asserted 0.66
s2 We construct an equivalence of categories between finite dimensional $\Bbb{F}_p$-representations of the product of $\Delta$ copies of the absolute Galois group of $K$ and multivariable \' etale $(\varphi, \Gamma)$-modules over a multivariable Laurent series ring over $k_K$. contribution 0.57 0.95 0.95 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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  • C citations
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Let $K$ be a complete discretely valued field with mixed characteristic $(0, p)$ and imperfect residue field $k_K$. Let $\Delta$ be a finite set. We construct an equivalence of categories between finite dimensional $\Bbb{F}_p$-representations of the product of $\Delta$ copies of the absolute Galois group of $K$ and multivariable \' etale $(\varphi, \Gamma)$-modules over a multivariable Laurent series ring over $k_K$.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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