Bibliographic record
Abstract
Abstract We compare the Iwasawa invariants of fine Selmer groups of p -adic Galois representations over admissible p -adic Lie extensions of a number field K to the Iwasawa invariants of ideal class groups along these Lie extensions. More precisely, let K be a number field, let V be a p -adic representation of the absolute Galois group $$G_K$$ of K , and choose a $$G_K$$ -invariant lattice $${T \subseteq V}$$ . We study the fine Selmer groups of $${A = V/T}$$ over suitable p -adic Lie extensions $$K_\infty /K$$ , comparing their corank and $$\mu $$ -invariant to the corank and the $$\mu $$ -invariant of the Iwasawa module of ideal class groups in $$K_\infty /K$$ . In the second part of the article, we compare the Iwasawa $$\mu $$ - and $$l_0$$ -invariants of the fine Selmer groups of CM modular forms on the one hand and the Iwasawa invariants of ideal class groups on the other hand over trivialising multiple $$\mathbb {Z}_p$$ -extensions of K .
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".