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The fullness conjectures for products of elliptic curves

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Bruno Kahn, with an appendix by Cyril Demarche

Number Theory · Submitted 12 Mar 2023

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

The authors' main claim We prove all conjectures from chapter 7 of Yves Andr\'e's book on motives in the case of products of elliptic curves.

how it is stated · asserted 1.00 read the record →

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arXiv ID2303.06690 (version 4)
Pith IDIT7CTFC7, Pith's permanent record of this paper and its review
CitationBruno Kahn, with an appendix by Cyril Demarche. "The fullness conjectures for products of elliptic curves." arXiv:2303.06690 (2023). https://pith.science/paper/IT7CTFC7
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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-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,224 input tokens.

What the abstract itself states, as probabilities: claims first 0.09 · states limitation 0.53 · human participants 0.01 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.92 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v4. Results and the main claim are underlined; .

We prove all conjectures from chapter 7 of Yves Andr\'e's book on motives in the case of products of elliptic curves. The proofs given here are simpler and more uniform than the previous proofs in known cases.

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 all conjectures from chapter 7 of Yves Andr\'e's book on motives in the case of products of elliptic curves. contribution 0.60 0.96 0.95 asserted 1.00
s1 The proofs given here are simpler and more uniform than the previous proofs in known cases. contribution 0.55 0.79 0.07 asserted 1.00

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

What was examined, and what was not

sources read
  • arXiv listing abstract v4
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • 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 all conjectures from chapter 7 of Yves Andr\'e's book on motives in the case of products of elliptic curves. The proofs given here are simpler and more uniform than the previous proofs in known cases.

Human review

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How the literature uses it

2 arXiv papers cite this in 3 sentences

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

What it cites · 2 sentences without a confident label

Compares with 1 paper
  • Since then, Mingmin Chen and Charles Vial have also proven the de Rham-Betti conjecture for products of elliptic curves in [ref] .

    2206.08618 · Introduction · 0.84

Cites as background 1 paper
  • See [ref] for a definition of $$ modulo other adequate equivalence relations and over not necessarily algebraically closed fields.

    Chow-Lefschetz motives · The separably closed case · 0.88

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