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Record W2798291480 · doi:10.2140/akt.2023.8.421

Fibrant resolutions for motivic Thom spectra

2023· article· en· W2798291480 on OpenAlexaff
Grigory Garkusha, Alexander Neshitov

Bibliographic record

VenueAnnals of K-Theory · 2023
Typearticle
Languageen
FieldMathematics
TopicHomotopy and Cohomology in Algebraic Topology
Canadian institutionsWestern University
Fundersnot available
KeywordsSpectral lineMathematicsPure mathematicsPhysicsAstronomy

Abstract

fetched live from OpenAlex

Using the theory of framed correspondences developed by Voevodsky [32] and the machinery of framed motives introduced and developed in [13], various explicit fibrant resolutions for a motivic Thom spectrum E are constructed in this paper.It is shown that the bispectrumin the category of bispectra.As a topological application, it is proved that the E-framed motive with finite coefficients M E (pt)(pt)/N, N > 0, of the point pt = Spec k evaluated at pt is a quasifibrant model of the topological S 2 -spectrum Re ε (E)/N whenever the base field k is algebraically closed of characteristic zero with an embedding ε : k ↩→ C. Furthermore, the algebraic cobordism spectrum MGL is computed in terms of Ω-correspondences in the sense of [21].It is also proved that MGL is represented by a bispectrum each term of which is a sequential colimit of simplicial smooth quasi-projective varieties.

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)0.001
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 score0.007
Threshold uncertainty score0.024

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0010.001
Meta-epidemiology (narrow)0.0010.000
Meta-epidemiology (broad)0.0000.001
Bibliometrics0.0030.001
Science and technology studies0.0020.002
Scholarly communication0.0020.003
Open science0.0010.004
Research integrity0.0010.002
Insufficient payload (model declined to judge)0.0070.001

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 head0.142
GPT teacher head0.399
Teacher spread0.257 · 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

Citations6
Published2023
Admission routes1
Has abstractyes

Explore more

Same venueAnnals of K-TheorySame topicHomotopy and Cohomology in Algebraic TopologyFrench-language works237,207