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Generalized Kato classes and exceptional zero conjectures
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Rivero Salgado, Oscar (2022) Generalized Kato classes and exceptional zero conjectures. Indiana University Mathematics Journal, 71 (2). pp. 649-684. doi:10.1512/iumj.2022.71.8921 ISSN 0222-2518.
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Official URL: http://dx.doi.org/10.1512/iumj.2022.71.8921
Abstract
The primary objective of this paper is the study of different instances of the elliptic Stark conjectures of Darmon, Lauder, and Rotger, in a situation where the elliptic curve attached to the modular form f has split multiplicative reduction at p and the arithmetic phenomena are specially rich. For that purpose, we resort to the principle of improved p-adic L-functions and study their L-invariants. We further interpret these in terms of derived cohomology classes coming from the setting of diagonal cycles, showing that the same L-invariant which arises in the theory of p-adic L-functions also governs the arithmetic of Euler systems. Thus, we can reduce, in the split multiplicative situation, the conjecture of Darmon, Lauder, and Rotger to a more familiar statement about higher-order derivatives of a triple product p-adic L-function at a point lying inside the region of classical interpolation, in the realm of the more well-known exceptional zero conjectures.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Arithmetical algebraic geometry, Stark's conjectures, L-functions, Number theory, p-adic numbers | ||||
| Journal or Publication Title: | Indiana University Mathematics Journal | ||||
| Publisher: | Indiana University Mathematics | ||||
| ISSN: | 0222-2518 | ||||
| Official Date: | 2022 | ||||
| Dates: |
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| Volume: | 71 | ||||
| Number: | 2 | ||||
| Page Range: | pp. 649-684 | ||||
| DOI: | 10.1512/iumj.2022.71.8921 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access | ||||
| Date of first compliant deposit: | 30 June 2022 | ||||
| Date of first compliant Open Access: | 30 June 2022 |
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