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Record W3154723035 · doi:10.1016/j.aim.2022.108638

Cohomology of the moduli stack of algebraic vector bundles

2022· article· en· W3154723035 on OpenAlexaff
Toni Annala, Ryomei Iwasa

Bibliographic record

VenueAdvances in Mathematics · 2022
Typearticle
Languageen
FieldMathematics
TopicAlgebraic Geometry and Number Theory
Canadian institutionsUniversity of British Columbia
FundersVäisälän RahastoH2020 Marie Skłodowska-Curie ActionsHorizon 2020Suomalainen TiedeakatemiaEuropean Commission
KeywordsMathematicsVector bundleStack (abstract data type)Chern classPure mathematicsSheafModuliMultiplicative functionRank (graph theory)CohomologyScheme (mathematics)Tautological line bundleModuli spaceAlgebra over a fieldCombinatoricsMathematical analysisNormal bundleFrame bundle

Abstract

fetched live from OpenAlex

Let Vectn be the moduli stack of vector bundles of rank n on derived schemes. We prove that, if E is a Zariski sheaf of ring spectra which is equipped with finite quasi-smooth transfers and satisfies projective bundle formula, then E⁎(Vectn,S) is freely generated by Chern classes c1,…,cn over E⁎(S) for any qcqs derived scheme S. Examples include all multiplicative localizing invariants.

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)0.001
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 score0.008
Threshold uncertainty score0.027

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0000.001
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0020.001
Science and technology studies0.0010.002
Scholarly communication0.0020.003
Open science0.0010.002
Research integrity0.0000.001
Insufficient payload (model declined to judge)0.0080.001

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 head0.019
GPT teacher head0.290
Teacher spread0.271 · 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

Citations4
Published2022
Admission routes1
Has abstractyes

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