Triangulable 𝒪<sub><i>F</i></sub>-analytic (<i>φ</i><sub><i>q</i></sub><i>,</i>Γ)-modules of rank 2
Bibliographic record
Abstract
The theory of (ϕ q , )-modules is a generalization of Fontaine's theory of (ϕ, )modules, which classifies G F -representations on O F -modules and F-vector spaces for any finite extension F of ޑ p .In this paper following Colmez's method we classify triangulable O F -analytic (ϕ q , )-modules of rank 2. In the process we establish two kinds of cohomology theories for O F -analytic (ϕ q , )modules.Using them, we show that if D is an étale O F -analytic (ϕ q , )-module such that D ϕ q =1, =1 = 0 (i.e., V G F = 0, where V is the Galois representation attached to D), then any overconvergent extension of the trivial representation of G F by V is O F -analytic.In particular, contrary to the case of F = ޑ p , there are representations of G F that are not overconvergent.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.003 | 0.001 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.012 | 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".