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Record W1973997298 · doi:10.1112/s0010437x13007318

Integral division points on curves

2013· article· en· W1973997298 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

fundA Canadian funder is recorded on the work.
no affNo Canadian affiliation: this work is invisible to an affiliation-only frame.
No Canadian affiliation. An affiliation-only frame, the usual design, would never have seen this work. It is one of the works that make the case for inverting the frame.

Bibliographic record

VenueCompositio Mathematica · 2013
Typearticle
Languageen
FieldMathematics
TopicAlgebraic Geometry and Number Theory
Canadian institutionsnot available
FundersConcordia UniversityUniversity of Texas at Austin
KeywordsMathematicsDivisor (algebraic geometry)Abelian groupAlgebraic number fieldConjectureCombinatoricsElliptic curveDivision (mathematics)Division ringTorsion (gastropod)Pure mathematicsArithmetic

Abstract

fetched live from OpenAlex

Abstract Let $k$ be a number field with algebraic closure $ \overline{k} $ , and let $S$ be a finite set of primes of $k$ containing all the infinite ones. Let $E/ k$ be an elliptic curve, ${\mit{\Gamma} }_{0} $ be a finitely generated subgroup of $E( \overline{k} )$ , and $\mit{\Gamma} \subseteq E( \overline{k} )$ the division group attached to ${\mit{\Gamma} }_{0} $ . Fix an effective divisor $D$ of $E$ with support containing either: (i) at least two points whose difference is not torsion; or (ii) at least one point not in $\mit{\Gamma} $ . We prove that the set of ‘integral division points on $E( \overline{k} )$ ’, i.e., the set of points of $\mit{\Gamma} $ which are $S$ -integral on $E$ relative to $D, $ is finite. We also prove the ${ \mathbb{G} }_{\mathrm{m} } $ -analogue of this theorem, thereby establishing the 1-dimensional case of a general conjecture we pose on integral division points on semi-abelian varieties.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesInsufficient payload (model declined to judge)
Consensus categoriesInsufficient payload (model declined to judge)
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.155
Threshold uncertainty score0.994

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0080.007

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.031
GPT teacher head0.294
Teacher spread0.263 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it