MétaCan
Menu
Back to cohort
Record W2604191110 · doi:10.1002/mana.201600529

Chow ring of generic flag varieties

2017· article· en· W2604191110 on OpenAlexaff
Nikita A. Karpenko

Bibliographic record

VenueMathematische Nachrichten · 2017
Typearticle
Languageen
FieldMathematics
TopicAlgebraic Geometry and Number Theory
Canadian institutionsUniversity of Alberta
Fundersnot available
KeywordsMathematicsFlag (linear algebra)Isomorphism (crystallography)ConjecturePure mathematicsFiltration (mathematics)Ring (chemistry)CombinatoricsEpimorphismSimple (philosophy)Algebraic groupVariety (cybernetics)Algebraic numberAlgebra over a fieldMathematical analysis

Abstract

fetched live from OpenAlex

Abstract Let G be a split semisimple algebraic group over a field k and let X be the flag variety (i.e., the variety of Borel subgroups) of G twisted by a generic G ‐torsor. We start a systematic study of the conjecture, raised in in form of a question, that the canonical epimorphism of the Chow ring of X onto the associated graded ring of the topological filtration on the Grothendieck ring of X is an isomorphism. Since the topological filtration in this case is known to coincide with the computable gamma filtration, this conjecture indicates a way to compute the Chow ring. We reduce its proof to the case of . For simply‐connected or adjoint G , we reduce the proof to the case of simple G . Finally, we provide a list of types of simple groups for which the conjecture holds. Besides of some classical types considered previously (namely, A, C, and the special orthogonal groups of types B and D), the list contains the exceptional types G 2 , F 4 , and simply‐connected E 6 .

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)0.001
metaresearch head score (Gemma)0.001
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 score0.194
Threshold uncertainty score0.874

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.001
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0010.000
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 head0.062
GPT teacher head0.311
Teacher spread0.249 · 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

Citations12
Published2017
Admission routes1
Has abstractyes

Explore more

Same venueMathematische NachrichtenSame topicAlgebraic Geometry and Number TheoryFrench-language works237,207