Bibliographic record
Abstract
Let F = ކ q (T ) and A = ކ q [T ].Given two nonisogenous rank-r Drinfeld A-modules φ and φ over K , where K is a finite extension of F, we obtain a partially explicit upper bound (dependent only on φ and φ ) on the degree of primes ℘ of K such that P ℘ (φ) = P ℘ (φ ), where P ℘ ( * ) denotes the characteristic polynomial of Frobenius at ℘ on a Tate module of * .The bounds are completely explicit in terms of the defining coefficients of φ and φ , except for one term, which can be made explicit in the case of r = 2.An ingredient in the proof of the partially explicit isogeny theorem for general rank is an explicit bound for the different divisor of torsion fields of Drinfeld modules, which detects primes of potentially good reduction.Our results are a Drinfeld module analogue of Serre's work (1981), but the results we obtain are unconditional because the generalized Riemann hypothesis holds for function fields.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.007 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.007 | 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".