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Repr\'esentations p-adiques et normes universelles, I. Le cas cristallin

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Bernadette Perrin-Riou

Number Theory · Submitted 17 Dec 1998

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

The authors' main claim Then, the projective limit of the H^1_g(K(\mu_{p^n}), T) is equal up to torsion to the projective limit of the H^1(K(\mu_{p^n}), Fil^1 T).

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arXiv IDmath/9812170 (version 1)
Pith IDJOP2WCQG, Pith's permanent record of this paper and its review
CitationBernadette Perrin-Riou. "Repr\'esentations p-adiques et normes universelles, I. Le cas cristallin." arXiv:math/9812170 (1998). https://pith.science/paper/JOP2WCQG
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,719 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.29 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.91 · compares with prior results 0.05 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

Let V be a crystalline p-adic representation of the absolute Galois group G_K of an finite unramified extension K of Q_p and T a lattice of V stable by G_K. We prove the following result: Let Fil^1 V be the maximal sub-representation of V with Hodge-Tate weights strictly positive and Fil^1 T=T \cap Fil^1 V. Then, the projective limit of the H^1_g(K(\mu_{p^n}), T) is equal up to torsion to the projective limit of the H^1(K(\mu_{p^n}), Fil^1 T). So its rank over the Iwasawa algebra is [K:Q_p] dim Fil^1 V.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Let V be a crystalline p-adic representation of the absolute Galois group G_K of an finite unramified extension K of Q_p and T a lattice of V stable by G_K. background 1.00 0.08 0.02 asserted 0.72
s1 We prove the following result: Let Fil^1 V be the maximal sub-representation of V with Hodge-Tate weights strictly positive and Fil^1 T=T \cap Fil^1 V. result 0.47 0.66 0.10 asserted 0.91
s2 Then, the projective limit of the H^1_g(K(\mu_{p^n}), T) is equal up to torsion to the projective limit of the H^1(K(\mu_{p^n}), Fil^1 T). result 1.00 0.89 0.87 asserted 1.00
s3 So its rank over the Iwasawa algebra is [K:Q_p] dim Fil^1 V. result 0.77 0.85 0.20 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

Let V be a crystalline p-adic representation of the absolute Galois group G_K of an finite unramified extension K of Q_p and T a lattice of V stable by G_K. We prove the following result: Let Fil^1 V be the maximal sub-representation of V with Hodge-Tate weights strictly positive and Fil^1 T=T \cap Fil^1 V. Then, the projective limit of the H^1_g(K(\mu_{p^n}), T) is equal up to torsion to the projective limit of the H^1(K(\mu_{p^n}), Fil^1 T). So its rank over the Iwasawa algebra is [K:Q_p] dim Fil^1 V.

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