On the elliptic stark conjecture at primes of multiplicative reduction
| Autor: | Daniele Casazza, Victor Rotger |
|---|---|
| Přispěvatelé: | Ministerio de Economía y Competitividad (España), European Commission, Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. TN - Grup de Recerca en Teoria de Nombres |
| Rok vydání: | 2019 |
| Předmět: |
Conjecture
Mathematics::Number Theory General Mathematics European research media_common.quotation_subject 010102 general mathematics Matemàtiques i estadística::Àlgebra [Àrees temàtiques de la UPC] 01 natural sciences Corbes Matemàtiques i estadística::Anàlisi numèrica [Àrees temàtiques de la UPC] Management Geometria algèbrica--Aritmètica 14 Algebraic geometry::14H Curves [Classificació AMS] Excellence 11 Number theory::11G Arithmetic algebraic geometry (Diophantine geometry) [Classificació AMS] media_common.cataloged_instance Christian ministry Arithmetical algebraic geometry 0101 mathematics European union Curves Mathematics media_common |
| Zdroj: | Digital.CSIC. Repositorio Institucional del CSIC instname UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) |
| Popis: | In [DLR], Darmon, Lauder, and Rotger formulated a p-adic elliptic Stark conjecture for the twist of an elliptic curve E/Q by the self-dual tensor product ρ ρ of two odd and two-dimensional Artin representations. These authors provided abundant numerical evidence and proved the conjecture in the special setting where p is a prime of good reduction for E and ρ and ρ2 are induced from finite-order characters ψ, ψ of the same imaginary quadratic field. The key step in their proof is a factorization of one-variable p-adic L-functions, where ψ varies in a p-adic family of Hecke characters. The main goal of this article is to prove a new case of the conjecture, placing ourselves in the setting where p is a prime of multiplicative reduction for E. In order to achieve our theorem, we need to work with two-variable p-adic L-functions, where the weight 2 cusp form associated with E also moves independently along a Hida family. Our main result then follows from a factorization of p-adic L-series extending to two variables the one obtained in [DLR]. On the way we also generalize to our setting the results obtained in [CR]. The two authors were supported by Spanish Grant MTM2015-63829-P. The first author acknowledges financial support by the Spanish Ministry of Economy and Competitiveness, through the Severo Ochoa programme for Centres of Excellence in R&D (SEV-2015-0554). The second author acknowledges financial support from the Spanish Ministry of Economy and Competitiveness, through the María de Maeztu Programme for Units of Excellence in R&D (MDM-2014-0445). This project has also received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 682152). Finally, the authors acknowledge financial support from the Spanish Ministry of Economy and Competitiveness, through the María de Maeztu Programme for Units of Excellence in R&D (MDM-2014-0445). |
| Databáze: | OpenAIRE |
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