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Record W1993455468 · doi:10.1515/crelle.2006.027

κ-types and Γ-asymptotic expansions

2006· article· de· W1993455468 on OpenAlexaff
Ju-Lee Kim, Fiona Murnaghan

Bibliographic record

VenueJournal für die reine und angewandte Mathematik (Crelles Journal) · 2006
Typearticle
Languagede
FieldMathematics
TopicAdvanced Algebra and Geometry
Canadian institutionsToronto Public HealthUniversity of Toronto
Fundersnot available
KeywordsMathematicsGeodetic datumType (biology)Pure mathematicsElement (criminal law)Domain (mathematical analysis)Character (mathematics)Field (mathematics)Representation (politics)Zero (linguistics)Irreducible representationMathematical analysisGeometry

Abstract

fetched live from OpenAlex

Let G be the k -rational points of a connected reductive k -group, where k is a p -adic field of characteristic zero. We define a notion of strongly good positive G -datum Σ, and construct a κ-type associated to such a datum, following the methods of Yu's construction of types. Suppose π is an irreducible admissible representation of G of positive depth, containing such a κ-type. Then assuming that the residual characteristic of k is sufficiently large, we prove that the character of π is Γ-asymptotic on a G -domain defined in terms of Σ, where Γ is a semisimple element naturally associated to Σ. We also obtain a domain of validity for the Shalika germ expansion around the element Γ.

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)0.000
metaresearch head score (Gemma)0.002
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 score0.003
Threshold uncertainty score0.009

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0000.002
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0010.000
Science and technology studies0.0010.002
Scholarly communication0.0010.002
Open science0.0000.002
Research integrity0.0000.001
Insufficient payload (model declined to judge)0.0030.000

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 head0.016
GPT teacher head0.296
Teacher spread0.280 · 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

Citations14
Published2006
Admission routes1
Has abstractyes

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Same venueJournal für die reine und angewandte Mathematik (Crelles Journal)Same topicAdvanced Algebra and GeometryFrench-language works237,207