Iwasawa theory of elliptic curves at supersingular primes over ℤ p -extensions of number fields
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Bibliographic record
Abstract
In this paper, we make a study of the Iwasawa theory of an elliptic curve at a supersingular prime p along an arbitrary Z(p)-extension of a number field K in the case when p splits completely in K. Generalizing work of Kobayashi and Perrin-Riou , we define restricted Selmer groups and lambda(+/-), mu(+/-)-invariants; we then derive asymptotic formulas describing the growth of the Selmer group in terms of these invariants. To be able to work with non-cyclotomic Z(p)-extensions, a new local result is proven that gives a complete description of the formal group of an elliptic curve at a supersingular prime along any ramified Z(p)-extension of Q(p).
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.007 | 0.000 |
Machine scores (provisional)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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