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Repr\'esentations modulaires de $\mathrm{GL}_2(\mathbf{Q}_p)$ et repr\'esentations galoisiennes de dimension 2

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Laurent Berger

Number Theory · Submitted 5 Oct 2005

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

The authors' main claim We prove Breuil's conjecture concerning the reduction modulo $p$ of trianguline representations $V$ and of the representations $\Pi(V)$ of $\mathrm{GL}_2(\mathbf{Q}_p)$ associated to them by the $p$-adic Langlands correspondence.

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arXiv IDmath/0510090 (version 1)
Pith IDZYXMQNBV, Pith's permanent record of this paper and its review
CitationLaurent Berger. "Repr\'esentations modulaires de $\mathrm{GL}_2(\mathbf{Q}_p)$ et repr\'esentations galoisiennes de dimension 2." arXiv:math/0510090 (2005). https://pith.science/paper/ZYXMQNBV
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,428 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.15 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We prove Breuil's conjecture concerning the reduction modulo $p$ of trianguline representations $V$ and of the representations $\Pi(V)$ of $\mathrm{GL}_2(\mathbf{Q}_p)$ associated to them by the $p$-adic Langlands correspondence. The main ingredient of the proof is the study of some smooth irreducible representations of $\mathrm{B}(\mathbf{Q}_p)$ through models built using the theory of $(\phi,\Gamma)$-modules.

background contribution method result interpretation main claim

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We prove Breuil's conjecture concerning the reduction modulo $p$ of trianguline representations $V$ and of the representations $\Pi(V)$ of $\mathrm{GL}_2(\mathbf{Q}_p)$ associated to them by the $p$-adic Langlands correspondence. result 0.75 0.96 0.95 asserted 1.00
s1 The main ingredient of the proof is the study of some smooth irreducible representations of $\mathrm{B}(\mathbf{Q}_p)$ through models built using the theory of $(\phi,\Gamma)$-modules. method 0.91 0.89 0.04 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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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

We prove Breuil's conjecture concerning the reduction modulo $p$ of trianguline representations $V$ and of the representations $\Pi(V)$ of $\mathrm{GL}_2(\mathbf{Q}_p)$ associated to them by the $p$-adic Langlands correspondence. The main ingredient of the proof is the study of some smooth irreducible representations of $\mathrm{B}(\mathbf{Q}_p)$ through models built using the theory of $(\phi,\Gamma)$-modules.

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