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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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
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spelling Characteristic ideals and Selmer groupsBandini, Andrea|||0000-0001-5876-348XBars Cortina, Francesc|||0000-0003-4779-3995Longhi, Ignazio|||0000-0002-1141-7018Characteristic idealsIwasawa theorySelmer groupsLet 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. 22015-01-0120152015-01-01Articlehttp://purl.org/coar/resource_type/c_6501SMURhttp://purl.org/coar/version/c_71e4c1898caa6e32info:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/240662https://dx.doi.org/urn:doi:10.1016/j.jnt.2015.05.011reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengMinisterio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2013-40680-Popen accesshttp://purl.org/coar/access_right/c_abf2Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.https://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2406622026-06-06T12:50:31Z
dc.title.none.fl_str_mv Characteristic ideals and Selmer groups
title Characteristic ideals and Selmer groups
spellingShingle Characteristic ideals and Selmer groups
Bandini, Andrea|||0000-0001-5876-348X
Characteristic ideals
Iwasawa theory
Selmer groups
title_short Characteristic ideals and Selmer groups
title_full Characteristic ideals and Selmer groups
title_fullStr Characteristic ideals and Selmer groups
title_full_unstemmed Characteristic ideals and Selmer groups
title_sort Characteristic ideals and Selmer groups
dc.creator.none.fl_str_mv Bandini, Andrea|||0000-0001-5876-348X
Bars Cortina, Francesc|||0000-0003-4779-3995
Longhi, Ignazio|||0000-0002-1141-7018
author Bandini, Andrea|||0000-0001-5876-348X
author_facet Bandini, Andrea|||0000-0001-5876-348X
Bars Cortina, Francesc|||0000-0003-4779-3995
Longhi, Ignazio|||0000-0002-1141-7018
author_role author
author2 Bars Cortina, Francesc|||0000-0003-4779-3995
Longhi, Ignazio|||0000-0002-1141-7018
author2_role author
author
dc.subject.none.fl_str_mv Characteristic ideals
Iwasawa theory
Selmer groups
topic Characteristic ideals
Iwasawa theory
Selmer groups
description 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.
publishDate 2015
dc.date.none.fl_str_mv 2
2015-01-01
2015
2015-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
SMUR
http://purl.org/coar/version/c_71e4c1898caa6e32
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/240662
https://dx.doi.org/urn:doi:10.1016/j.jnt.2015.05.011
url https://ddd.uab.cat/record/240662
https://dx.doi.org/urn:doi:10.1016/j.jnt.2015.05.011
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2013-40680-P
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
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