CM cycles on Kuga-Sato varieties over Shimura curves and Selmer groups
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 enjoyi...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/175972 |
| Acceso en línea: | https://hdl.handle.net/2117/175972 https://dx.doi.org/10.1515/forum-2017-0008 |
| Access Level: | acceso abierto |
| Palabra clave: | Manifolds (Mathematics) Curves, Modular Arithmetical algebraic geometry Varietats (Matemàtica) Varietats de Shimura Corbes modulars Geometria algebraica aritmètica Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria |
| Sumario: | 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 [21], as adapted by Nekova´¿r [28] 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. |
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