On a <i>p</i>-adic invariant cycles theorem
Bibliographic record
Abstract
Abstract For a proper semistable curve X over a DVR of mixed characteristics and perfect residue field we prove the “invariant cycles theorem” with trivial coefficients, i.e. that the group of elements of the first de Rham cohomology group of the generic fiber of X annihilated by the monodromy operator coincides with the first rigid cohomology group of its special fiber. This is done using an explicit description of the monodromy operator on the de Rham cohomology of the generic fiber of X with coefficients a convergent F -isocrystal (see [Représentations p -adiques de groupes p -adiques III: Méthodes globales et géométriques, Astérisque 331, 179–254]) and the proof exhibits an interesting interplay between this cohomology group and the combinatorics of the graph of the reduction of X . The result was proved in a different way in the case the DVR has finite residue field in [Duke Math. J. 97 (1999), no. 1, 155–169]. We also study the case where the coefficients are unipotent convergent F -isocrystals on the special fiber of X (without log-structure): we show that the invariant cycles theorem does not hold in general in this setting and give a sufficient condition for non-exactness.
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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 | 0.006 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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 teacher head, 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".