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Record W2051590578 · doi:10.4153/cjm-2002-012-x

On Connected Components of Shimura Varieties

2002· article· en· W2051590578 on OpenAlexaff
Thomas J. Haines

Bibliographic record

VenueCanadian Journal of Mathematics · 2002
Typearticle
Languageen
FieldMathematics
TopicAdvanced Algebra and Geometry
Canadian institutionsUniversity of Toronto
Fundersnot available
KeywordsMathematicsInvariant (physics)TRACE (psycholinguistics)Pure mathematicsCohomologyGroup (periodic table)Shimura varietyHecke algebraOperator (biology)Character (mathematics)Algebra over a fieldModular formGeometryMathematical physics

Abstract

fetched live from OpenAlex

Abstract We study the cohomology of connected components of Shimura varieties coming from the group GSp 2g , by an approach modeled on the stabilization of the twisted trace formula, due to Kottwitz and Shelstad. More precisely, for each character ϖ on the group of connected components of we define an operator L ( ω ) on the cohomology groups with compact supports H i c ( , ), and then we prove that the virtual trace of the composition of L ( ω ) with a Hecke operator f away from p and a sufficiently high power of a geometric Frobenius , can be expressed as a sum of ω - weighted (twisted) orbital integrals (where ω - weighted means that the orbital integrals and twisted orbital integrals occuring here each have a weighting factor coming from the character ϖ ). As the crucial step, we define and study a new invariant α 1 ( γ 0 ; γ, δ ) which is a refinement of the invariant α ( γ 0 ; γ, δ ) defined by Kottwitz. This is done by using a theorem of Reimann and Zink.

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)0.000
metaresearch head score (Gemma)0.002
Version: codex-gemma-dda1882f352aValidation 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 score0.024
Threshold uncertainty score0.987

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.002
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0010.000

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 head0.067
GPT teacher head0.263
Teacher spread0.196 · 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 teacher head, 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

Citations5
Published2002
Admission routes1
Has abstractyes

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