Bibliographic record
Abstract
If K / k is a finite Galois extension of number fields with Galois group G , then the kernel of the capitulation map C l k → C l K of ideal class groups is isomorphic to the kernel X ( H ) of the transfer map H / H ' → A , where H = Gal ( K ˜ / k ) , A = Gal ( K ˜ / K ) and K ˜ is the Hilbert class field of K . H. Suzuki proved that when G is abelian, | G | divides | X ( H ) | . We call a finite abelian group X a transfer kernel for G if X ≅ X ( H ) for some group extension A ↪ H ↠ G . After characterizing transfer kernels in terms of integral representations of G , we show that X is a transfer kernel for the abelian group G if and only if | G | X = 0 and | G | divides | X | . Our arguments give a new proof of Suzuki’s result.
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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 | 0.001 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.005 | 0.007 |
| Open science | 0.001 | 0.004 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.024 | 0.007 |
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".