On the Mordell-Weil ranks of supersingular abelian varieties in cyclotomic extensions
Bibliographic record
Abstract
Let F F be a number field unramified at an odd prime p p and let F ∞ F_\infty be the Z p \mathbf {Z}_p -cyclotomic extension of F F . Let A A be an abelian variety defined over F F with good supersingular reduction at all primes of F F above p p . Büyükboduk and the first named author have defined modified Selmer groups associated to A A over F ∞ F_\infty . Assuming that the Pontryagin dual of these Selmer groups is a torsion Z p [ [ Gal ( F ∞ / F ) ] ] \mathbf {Z}_p[[\textrm {Gal}(F_\infty /F)]] -module, we give an explicit sufficient condition for the rank of the Mordell-Weil group A ( F n ) A(F_n) to be bounded as n n varies.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.004 | 0.002 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.019 | 0.003 |
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".