Characteristic ideals and Selmer groups
Let A be an abelian variety defined over a global field F of positive characteristic p and let F/F be a ZpN-extension, unramified outside a finite set of places of F. Assuming that all ramified places are totally ramified, we define a pro-characteristic ideal associated to the Pontrjagin dual of the...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:240662 |
| Acceso en línea: | https://ddd.uab.cat/record/240662 https://dx.doi.org/urn:doi:10.1016/j.jnt.2015.05.011 |
| Access Level: | acceso abierto |
| Palabra clave: | Characteristic ideals Iwasawa theory Selmer groups |
| Sumario: | Let A be an abelian variety defined over a global field F of positive characteristic p and let F/F be a ZpN-extension, unramified outside a finite set of places of F. Assuming that all ramified places are totally ramified, we define a pro-characteristic ideal associated to the Pontrjagin dual of the p-primary Selmer group of A. To do this we first show the relation between the characteristic ideals of duals of Selmer groups for a Zpd-extension Fd/F and for any Zpd-1-extension contained in Fd, and then use a limit process. Finally, we give an application to an Iwasawa Main Conjecture for the non-noetherian commutative Iwasawa algebra Zp[[Gal(F/F)]] in the case A is a constant abelian variety. |
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