Mini-Workshop: Thick Subcategories - Classifications and Applications
Bibliographic record
Abstract
Thick subcategories of triangulated categories have been the main topic of this workshop. Triangulated categories arise in many areas of modern mathematics, for instance in algebraic geometry, in representation theory of groups and algebras, or in stable homotopy theory. We give three typical examples of such triangulated categories: In each case, there is a classification of thick subcategories under some appropriate conditions. Recall that a subcategory of a triangulated category is thick , if it is a triangulated subcategory and closed under taking direct factors. Historically, the first classification has been established by Hopkins and Smith for the stable homotopy category, using the nilpotence theorem. A similar idea was then applied by Hopkins and Neeman to categories of perfect complexes over commutative noetherian rings. Later, Thomason extended this classification to schemes. For stable categories of finite group representations, the classification of thick subcategories is due to Benson, Carlson, and Rickard. The format of the workshop has been a combination of introductory survey lectures and more specialized talks on recent progress and open problems. The mix of participants from different mathematical areas and the relatively small size of the workshop provided an ideal atmosphere for fruitful interaction and exchange of ideas. It is a pleasure to thank the administration and the staff of the Oberwolfach Institute for their efficient support and hospitality.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot 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.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.005 | 0.005 |
| Open science | 0.003 | 0.006 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.037 | 0.014 |
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
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".