Derivatives of Beilinson–Flach classes, Gross–Stark formulas and a $p$-adic Harris–Venkatesh conjecture
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
We propose an alternative approach to the study of exceptional zeros from the point of view of Euler systems. As a first application, we give a new proof of a conjecture of Darmon, Lauder and Rotger regarding the computation of the \mathcal{L} -invariant of the adjoint of a weight one modular form in terms of units and p -units. While in our previous work with Rotger the essential ingredient was the use of Galois deformations techniques, we discuss a new method exclusively using the properties of Beilinson–Flach classes. One of the key ingredients is the computation of a cyclotomic derivative of a cohomology class in the framework of Perrin-Riou theory, which can be seen as a counterpart to the earlier work of Loeffler, Venjakob, and Zerbes. In our second application, we illustrate how these techniques could lead to a better understanding of this setting by introducing a new motivic p -adic L -function whose special values encode information just about the unit of the adjoint (and not also the p -unit), in the spirit of the conjectures of Harris and Venkatesh. We further discuss conjectural connections with the arithmetic of triple products of Coleman families.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 | 0.001 |
| 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 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it