CM cycles on Kuga-Sato varieties over Shimura curves and Selmer groups
| Autor: | Carlos de Vera-Piquero, Yara Elias |
|---|---|
| Přispěvatelé: | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Selmer group Galois cohomology Mathematics::Number Theory General Mathematics Modular form 01 natural sciences 11G18 (11G40 11R34 11F80) Manifolds (Mathematics) Corbes modulars 0103 physical sciences FOS: Mathematics Varietats de Shimura Geometria algebraica aritmètica Number Theory (math.NT) 0101 mathematics Mathematics Mathematics - Number Theory Applied Mathematics Varietats (Matemàtica) 010102 general mathematics Euler system Cohomology Curves Modular Mathematik Quadratic field Arithmetical algebraic geometry 010307 mathematical physics Matemàtiques i estadística::Geometria [Àrees temàtiques de la UPC] |
| Zdroj: | Forum Mathematicum UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) Recercat. Dipósit de la Recerca de Catalunya instname |
| Popis: | Given a modular form f of even weight larger than two and an imaginary quadratic field K satisfying a relaxed Heegner hypothesis, we construct a collection of CM cycles on a Kuga-Sato variety over a suitable Shimura curve which gives rise to a system of Galois cohomology classes attached to f enjoying the compatibility properties of an Euler system. Then we use Kolyvagin's method, as adapted by Nekovar to higher weight modular forms, to bound the size of the relevant Selmer group associated to f and K and prove the finiteness of the (primary part) of the Shafarevich-Tate group, provided that a suitable cohomology class does not vanish. 29 pages |
| Databáze: | OpenAIRE |
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