Periods of Modular GL2-type Abelian Varieties and p-adic Integration
Let F be a number field and an integral ideal. Let f be a modular newform over F of level with rational Fourier coefficients. Under certain additional conditions, Guitart and colleagues [Guitart et al. 16[Guitart et al. 16] X. Guitart, M. Masdeu, and M. Haluk Şengün. "Uniformization of Modular...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2445/142925 |
| Acceso en línea: | https://hdl.handle.net/2445/142925 |
| Access Level: | acceso abierto |
| Palabra clave: | Corbes el·líptiques Corbes sobre superfícies Elliptic curves Curves on surfaces |
| Sumario: | Let F be a number field and an integral ideal. Let f be a modular newform over F of level with rational Fourier coefficients. Under certain additional conditions, Guitart and colleagues [Guitart et al. 16[Guitart et al. 16] X. Guitart, M. Masdeu, and M. Haluk Şengün. "Uniformization of Modular Elliptic Curves via p-adic Periods." J. Algebra 445 (2016), 458-502. MR 3418066 [Crossref], [Web of Science ®] , [Google Scholar] ] constructed a p-adic lattice which is conjectured to be the Tate lattice of an elliptic curve Ef whose L-function equals that of f. The aim of this note is to generalize this construction when the Hecke eigenvalues of f generate a number field of degree d ⩾ 1, in which case the geometric object associated with f is expected to be, in general, an abelian variety Af of dimension d. We also provide numerical evidence supporting the conjectural construction in the case of abelian surfaces. |
|---|