Strongly modular models of Q-curves
| Autor: | Peter Bruin, Andrea Ferraguti |
|---|---|
| Přispěvatelé: | Bruin, Peter, Ferraguti, Andrea |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Galois cohomology 010103 numerical & computational mathematics 01 natural sciences quadratic twist Q-curve Q-curves Computer Science::General Literature 0101 mathematics quadratic twists ComputingMilieux_MISCELLANEOUS Mathematics Algebra and Number Theory business.industry strong modularity Computer Science::Information Retrieval 010102 general mathematics Astrophysics::Instrumentation and Methods for Astrophysics Complex multiplication Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) Modular design TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ComputingMethodologies_DOCUMENTANDTEXTPROCESSING Settore MAT/03 - Geometria business |
| Zdroj: | International Journal of Number Theory, 15(3), 505-526. World Scientific Pub Co Pte Lt |
| Popis: | Let [Formula: see text] be a [Formula: see text]-curve without complex multiplication. We address the problem of deciding whether [Formula: see text] is geometrically isomorphic to a strongly modular [Formula: see text]-curve. We show that the question has a positive answer if and only if [Formula: see text] has a model that is completely defined over an abelian number field. Next, if [Formula: see text] is completely defined over a quadratic or biquadratic number field [Formula: see text], we classify all strongly modular twists of [Formula: see text] over [Formula: see text] in terms of the arithmetic of [Formula: see text]. Moreover, we show how to determine which of these twists come, up to isogeny, from a subfield of [Formula: see text]. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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