Bibliographic record
Abstract
Iwasawa theory began as a Galois module theory of ideal class groups, initiated by Kenkichi Iwasawa as part of the theory of cyclotomic fields. In the early 1970s, Barry Mazur considered generalizations of Iwasawa theory to Selmer groups of elliptic curves (Abelian varieties in general). At the turn of this century, Coates and Sujatha initiated the study of a subgroup of the Selmer group of an elliptic curve called the fine Selmer group. The focus of this thesis is to understand arithmetic properties of this subgroup. In particular, we understand the structure of fine Selmer groups and their growth patterns. We investigate a strong analogy between the growth of the p-rank of the fine Selmer group and the growth of the p-rank of the class groups. This is done in the classical Iwasawa theoretic setting of (multiple) Zp-extensions; but what is more striking is that this analogy can be extended to non-p-adic analytic extensions as well, where standard Iwasawa theoretic tools fail. Coates and Sujatha proposed two conjectures on the structure of the fine Selmer groups. Conjecture A is viewed as a generalization of the classical Iwasawa μ=0 conjecture to the context of the motive associated to an elliptic curve; whereas Conjecture B is in the spirit of generalising Greenberg's pseudonullity conjecture to elliptic curves. We provide new evidence towards these two conjectures.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".