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Lefschetz for local Picard groups

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Bhargav Bhatt, Aise Johan de Jong

Algebraic Geometry · Submitted 13 Feb 2013

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

The authors' main claim We prove a strengthening of the Grothendieck-Lefschetz hyperplane theorem for local Picard groups conjectured by Koll\'ar.

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arXiv ID1302.3189 (version 1)
Pith IDW25AU2W5, Pith's permanent record of this paper and its review
CitationAise Johan de Jong, Bhargav Bhatt. "Lefschetz for local Picard groups." arXiv:1302.3189 (2013). https://pith.science/paper/W25AU2W5
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,274 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.63 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We prove a strengthening of the Grothendieck-Lefschetz hyperplane theorem for local Picard groups conjectured by Koll\'ar. Our approach, which relies on acyclicity results for absolute integral closures, also leads to a restriction theorem for higher rank bundles on projective varieties in positive characteristic.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We prove a strengthening of the Grothendieck-Lefschetz hyperplane theorem for local Picard groups conjectured by Koll\'ar. result 0.55 0.96 0.92 asserted 1.00
s1 Our approach, which relies on acyclicity results for absolute integral closures, also leads to a restriction theorem for higher rank bundles on projective varieties in positive characteristic. result 0.63 0.95 0.13 asserted 0.98

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

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not examined
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  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • T body sentences
  • C citations
  • R cross-paper relations

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 a strengthening of the Grothendieck-Lefschetz hyperplane theorem for local Picard groups conjectured by Koll\'ar. Our approach, which relies on acyclicity results for absolute integral closures, also leads to a restriction theorem for higher rank bundles on projective varieties in positive characteristic.

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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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