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Abelian Varieties over Cyclic Fields

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Bo-Hae Im, Michael Larsen

Number Theory · Submitted 16 May 2006

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

The authors' main claim If K is not locally finite, the rank of A over K is infinite.

how it is stated · asserted 1.00 read the record →

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arXiv IDmath/0605444 (version 3)
Pith ID7JZF4HBY, Pith's permanent record of this paper and its review
CitationBo-Hae Im, Michael Larsen. "Abelian Varieties over Cyclic Fields." arXiv:math/0605444 (2006). https://pith.science/paper/7JZF4HBY
Claim paper

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, 3,426 input tokens.

What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.15 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.34 · compares with prior results 0.03 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

Let K be a field not of characteristic 2 such that every finite separable extension of K is cyclic. Let A be an abelian variety over K. If K is infinite, then A(K) is Zariski-dense in A. If K is not locally finite, the rank of A over K is infinite.

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 Let K be a field not of characteristic 2 such that every finite separable extension of K is cyclic. background 0.99 0.07 0.02 asserted 0.72
s1 Let A be an abelian variety over K. background 0.92 0.05 0.02 unclear 0.71
s2 If K is infinite, then A(K) is Zariski-dense in A. result 1.00 0.62 0.30 asserted 1.00
s3 If K is not locally finite, the rank of A over K is infinite. result 1.00 0.66 0.32 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

What was examined, and what was not

sources read
  • arXiv listing abstract v3
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

Let K be a field not of characteristic 2 such that every finite separable extension of K is cyclic. Let A be an abelian variety over K. If K is infinite, then A(K) is Zariski-dense in A. If K is not locally finite, the rank of A over K is infinite.

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