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Record W4413187431 · doi:10.1112/blms.70166

Arithmetic sparsity in mixed Hodge settings

2025· article· en· W4413187431 on OpenAlexaff
Kenneth Chung Tak Chiu

Bibliographic record

VenueBulletin of the London Mathematical Society · 2025
Typearticle
Languageen
FieldMathematics
TopicAlgebraic Geometry and Number Theory
Canadian institutionsUniversity of Toronto
Fundersnot available
KeywordsMathematicsArithmeticAlgebra over a fieldPure mathematics

Abstract

fetched live from OpenAlex

Abstract Let be a smooth irreducible quasi‐projective algebraic variety over a number field . Suppose is equipped with a ‐adic étale local system compatible with an admissible graded‐polarized variation of mixed Hodge structures on the complex analytification of . We prove that the ‐integral points in are covered by subpolynomially many geometrically irreducible ‐subvarieties, each lying in a fiber of the mixed period mapping arising from the variation of mixed Hodge structures. This is based on recent works by Brunebarbe–Maculan and Ellenberg–Lawrence–Venkatesh. As an application, we prove that there are subpolynomially many ‐integral Laurent polynomials with fixed reflexive Newton polyhedron and fixed non‐zero principal ‐determinant. Our results answer a question asked by Ellenberg–Lawrence–Venkatesh.

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.

How this classification was reachedexpand

Full frame machine prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.001
Version: metacan-v3-hybrid-931329e0061cValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
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 score0.004
Threshold uncertainty score0.013

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0010.001
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0010.001
Science and technology studies0.0010.002
Scholarly communication0.0020.002
Open science0.0000.002
Research integrity0.0000.001
Insufficient payload (model declined to judge)0.0040.000

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 head0.015
GPT teacher head0.260
Teacher spread0.245 · 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

Classification

machine, unvalidated

Machine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
Study designTheoretical or conceptual
Domainnot available
GenreEmpirical

How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".

Quick stats

Citations1
Published2025
Admission routes1
Has abstractyes

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Same venueBulletin of the London Mathematical SocietySame topicAlgebraic Geometry and Number TheoryFrench-language works237,207