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Record W2034907533 · doi:10.3836/tjm/1327931394

On Stronger Versions of Brumer's Conjecture

2011· article· en· W2034907533 on OpenAlexaff
Masato Kurihara

Bibliographic record

VenueTokyo Journal of Mathematics · 2011
Typearticle
Languageen
FieldMathematics
TopicAdvanced Algebra and Geometry
Canadian institutionsToronto Metropolitan University
Fundersnot available
KeywordsAnnihilatorMathematicsIdeal (ethics)ConjectureCharacter (mathematics)Abelian groupField (mathematics)Dual (grammatical number)Pure mathematicsGroup (periodic table)Element (criminal law)Class (philosophy)Algebra over a fieldCombinatoricsDiscrete mathematicsLawGeometryPhilosophyEpistemologyPhysics

Abstract

fetched live from OpenAlex

Let $k$ be a totally real number field and $L$ a CM-field such that $L/k$ is finite and abelian. In this paper, we study a stronger version of Brumer's conjecture that the Stickelberger element times the annihilator of the group of roots of unity in $L$ is in the Fitting ideal of the ideal class group of $L$, and also study the dual version. We mainly study the Teichmüller character component, and determine the Fitting ideal in a certain case. We will see that these stronger versions hold in a certain case. It is known that the stronger version (SB) does not hold in general. We will prove in this paper that the dual version (DSB) does not hold in general, either.

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)0.006
metaresearch head score (Gemma)0.015
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 score0.013
Threshold uncertainty score0.045

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0060.015
Meta-epidemiology (narrow)0.0010.001
Meta-epidemiology (broad)0.0020.002
Bibliometrics0.0020.002
Science and technology studies0.0020.007
Scholarly communication0.0030.014
Open science0.0020.005
Research integrity0.0030.005
Insufficient payload (model declined to judge)0.0130.001

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 head0.069
GPT teacher head0.301
Teacher spread0.232 · 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

Citations7
Published2011
Admission routes1
Has abstractyes

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Same venueTokyo Journal of MathematicsSame topicAdvanced Algebra and GeometryFrench-language works237,207