Courbes hyperelliptiques à multiplications réelles et une construction de Shih
Bibliographic record
Abstract
Résumé Soient r et p deux nombres premiers distincts, soit , et soit 𝔽 le corps résiduel de K en une place au-dessus de p . Lorsque l’image de dans 𝔽 n’est pas un carré, nous donnons une construction géométrique d’une extension réguliere de K(t) de groupe de Galois PSL 2 (𝔽). Cette extension correspond à un revêtement de de « signature ( r, p, p ) » au sens de [3, sec. 6.3], et son existence est prédite par le critère de rigidité de Belyi, Fried, Thompson et Matzat. Sa construction s’obtient en tordant la representation galoisienne associée aux points d’ordre p d’une famille de variétés abéliennes à multiplications réelles par K découverte par Tautz, Top et Verberkmoes [6]. Ces variétés abéliennes sont définies sur un corps quadratique, et sont isogènes à leur conjugué galoisien. Notre construction généralise une méthode de Shih [4], [5], que l’on retrouve quand r = 2 et r = 3.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.263 | 0.066 |
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; both teacher heads agree on what is shown here.
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".