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Record W2609441945 · doi:10.1093/imrn/rnz178

Derived Equivalences for Symplectic Reflection Algebras

2019· preprint· en· W2609441945 on OpenAlexaff
Ivan Losev

Bibliographic record

VenueInternational Mathematics Research Notices · 2019
Typepreprint
Languageen
FieldMathematics
TopicAlgebraic structures and combinatorial models
Canadian institutionsUniversity of Toronto
FundersNational Research University Higher School of EconomicsNational Science Foundation
KeywordsSymplectic geometryPure mathematicsFunctorMathematicsReflection (computer programming)SheafSketchCoherent sheafAlgebra over a fieldGravitational singularitySimple (philosophy)Mathematical analysisComputer scienceEpistemology

Abstract

fetched live from OpenAlex

Abstract In this paper we study derived equivalences for symplectic reflection algebras. We establish a version of the derived localization theorem between categories of modules over these algebras and categories of coherent sheaves over quantizations of $\mathbb{Q}$-factorial terminalizations of the symplectic quotient singularities. To do this we construct a Procesi sheaf on the terminalization and show that the quantizations of the terminalization are simple sheaves of algebras. We will also sketch some applications to the generalized Bernstein inequality and to perversity of wall crossing functors.

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)0.003
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 score0.011
Threshold uncertainty score0.035

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0020.003
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.001
Bibliometrics0.0020.001
Science and technology studies0.0010.004
Scholarly communication0.0030.007
Open science0.0010.005
Research integrity0.0010.003
Insufficient payload (model declined to judge)0.0110.001

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 head0.316
GPT teacher head0.500
Teacher spread0.183 · 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

Citations2
Published2019
Admission routes1
Has abstractyes

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