Bibliographic record
Abstract
We study the growth of the p -primary fine Selmer group, R ( E / F ′ ) , of an elliptic curve over an intermediate sub-extension F ′ of a p -adic Lie extension, ℒ / F . We estimate the ℤ p -corank of the kernel and cokernel of the restriction map r ℒ / F ′ : R ( E / F ′ ) → R ( E / ℒ ) Gal ( ℒ / F ′ ) with F ′ a finite extension of F contained in ℒ . We show that the growth of the fine Selmer groups in these intermediate sub-extension is related to the structure of the fine Selmer group over the infinite level. On specializing to certain (possibly non-commutative) p -adic Lie extensions, we prove finiteness of the kernel and cokernel and provide growth estimates on their orders.
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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 | 0.002 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.005 | 0.002 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.004 | 0.007 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.016 | 0.001 |
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.
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".