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Record W2051800858 · doi:10.1515/crelle.2007.010

Massey products and ideal class groups

2007· article· de· W2051800858 on OpenAlexaff
Romyar T. Sharifi

Bibliographic record

VenueJournal für die reine und angewandte Mathematik (Crelles Journal) · 2007
Typearticle
Languagede
FieldMathematics
TopicAlgebraic Geometry and Number Theory
Canadian institutionsMcMaster University
Fundersnot available
KeywordsMathematicsCyclotomic fieldAbelian extensionAbelian groupGalois extensionPure mathematicsAlgebraic number fieldGalois groupGalois moduleGenus fieldQuotientRoot of unityExtension (predicate logic)Galois cohomologyDiscrete mathematics

Abstract

fetched live from OpenAlex

We consider certain Massey products in the cohomology of a Galois extension of fields with coefficients in p-power roots of unity. We prove formulas for these products both in general and in the special case that the Galois extension in question is the maximal extension of a number field unramified outside a set of primes S including those above p and any archimedean places. We then consider those Zp-Kummer extensions L ∞ of the maximal p-cyclotomic extension K ∞ of a number field K that are unramified outside S. We show that Massey products describe the structure of a certain “decomposition-free ” quotient of a graded piece of the maximal unramified abelian pro-p extension of L ∞ in which all primes above those in S split completely, with the grading arising from the augmentation filtration on the group ring of the Galois group of L∞/K∞. We explicitly describe examples of the maximal unramified abelian pro-p extensions of unramified outside p Kummer extensions of the cyclotomic field of all p-power roots of unity, for irregular primes p.

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 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)0.017
metaresearch head score (Gemma)0.003
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow), Science and technology studies, Scholarly communication, Research integrity, Insufficient payload (model declined to judge)
Consensus categoriesMeta-epidemiology (narrow)
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 score0.261
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0170.003
Meta-epidemiology (narrow)0.0020.001
Meta-epidemiology (broad)0.0020.001
Bibliometrics0.0010.001
Science and technology studies0.0020.001
Scholarly communication0.0020.001
Open science0.0010.001
Research integrity0.0010.005
Insufficient payload (model declined to judge)0.0010.001

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 head0.023
GPT teacher head0.299
Teacher spread0.276 · 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; both teacher heads agree on what is shown here.

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

Citations43
Published2007
Admission routes1
Has abstractyes

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