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Elimination of ramification I: The generalized stability theorem

2010· article· en· W2071231271 on OpenAlexafffund
Franz‐Viktor Kuhlmann

Bibliographic record

VenueTransactions of the American Mathematical Society · 2010
Typearticle
Languageen
FieldMathematics
TopicAlgebraic Geometry and Number Theory
Canadian institutionsUniversity of Saskatchewan
FundersNatural Sciences and Engineering Research Council of CanadaUniversität Konstanz
KeywordsMathematicsUniformization (probability theory)RamificationTranscendental numberExtension (predicate logic)Pure mathematicsStability theoremField (mathematics)Stability (learning theory)Discrete mathematicsMathematical analysis

Abstract

fetched live from OpenAlex

We prove a general version of the “Stability Theorem”: if K K is a valued field such that the ramification theoretical defect is trivial for all of its finite extensions, and if F | K F|K is a finitely generated (transcendental) extension of valued fields for which equality holds in the Abhyankar inequality, then the defect is also trivial for all finite extensions of F F . This theorem is applied to eliminate ramification in such valued function fields. It has applications to local uniformization and to the model theory of valued fields in positive characteristic.

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)0.002
metaresearch head score (Gemma)0.005
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: none
Teacher disagreement score0.012
Threshold uncertainty score0.040

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0020.005
Meta-epidemiology (narrow)0.0010.000
Meta-epidemiology (broad)0.0010.002
Bibliometrics0.0010.001
Science and technology studies0.0020.004
Scholarly communication0.0020.006
Open science0.0020.005
Research integrity0.0010.003
Insufficient payload (model declined to judge)0.0120.002

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 head0.024
GPT teacher head0.288
Teacher spread0.264 · 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

Citations36
Published2010
Admission routes2
Has abstractyes

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Same venueTransactions of the American Mathematical SocietySame topicAlgebraic Geometry and Number TheoryFrench-language works237,207