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...

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Detalles Bibliográficos
Autores: Bandini, Andrea|||0000-0001-5876-348X, Bars Cortina, Francesc|||0000-0003-4779-3995, Longhi, Ignazio|||0000-0002-1141-7018
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
Descripción
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.