Aspects of Iwasawa theory over function fields

We consider ZNp-extensions F of a global function field F and study various aspects of Iwasawa theory with emphasis on the two main themes already (and still) developed in the number fields case as well. When dealing with the Selmer group of an abelian variety A defined over F, we provide all the in...

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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: capítulo de libro
Fecha de publicación:2020
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:243142
Acceso en línea:https://ddd.uab.cat/record/243142
https://dx.doi.org/urn:doi:10.4171/198-1/7
Access Level:acceso abierto
Palabra clave:Iwasawa Main Conjecture
Global function fields
L-functions
Selmer groups
Class groups
Bernoulli-Carlitz numbers
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spelling Aspects of Iwasawa theory over function fieldsBandini, Andrea|||0000-0001-5876-348XBars Cortina, Francesc|||0000-0003-4779-3995Longhi, Ignazio|||0000-0002-1141-7018Iwasawa Main ConjectureGlobal function fieldsL-functionsSelmer groupsClass groupsBernoulli-Carlitz numbersWe consider ZNp-extensions F of a global function field F and study various aspects of Iwasawa theory with emphasis on the two main themes already (and still) developed in the number fields case as well. When dealing with the Selmer group of an abelian variety A defined over F, we provide all the ingredients to formulate an Iwasawa Main Conjecture relating the Fitting ideal and the p-adic L-function associated to A and F. We do the same, with characteristic ideals and p-adic L-functions, in the case of class groups (using known results on characteristic ideals and Stickelberger elements for Zdp-extensions). The final section provides more details for the cyclotomic ZNp-extension arising from the torsion of the Carlitz module: in particular, we relate cyclotomic units with Bernoulli-Carlitz numbers by a Coates-Wiles homomorphism.European Mathematical Society Publishing House 22020-01-0120202020-01-01Capítol de llibrehttp://purl.org/coar/resource_type/c_3248AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/bookPartapplication/pdfhttps://ddd.uab.cat/record/243142https://dx.doi.org/urn:doi:10.4171/198-1/7reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengMinisterio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM2009-10359open accesshttp://purl.org/coar/access_right/c_abf2Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.https://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2431422026-06-06T12:50:31Z
dc.title.none.fl_str_mv Aspects of Iwasawa theory over function fields
title Aspects of Iwasawa theory over function fields
spellingShingle Aspects of Iwasawa theory over function fields
Bandini, Andrea|||0000-0001-5876-348X
Iwasawa Main Conjecture
Global function fields
L-functions
Selmer groups
Class groups
Bernoulli-Carlitz numbers
title_short Aspects of Iwasawa theory over function fields
title_full Aspects of Iwasawa theory over function fields
title_fullStr Aspects of Iwasawa theory over function fields
title_full_unstemmed Aspects of Iwasawa theory over function fields
title_sort Aspects of Iwasawa theory over function fields
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 Iwasawa Main Conjecture
Global function fields
L-functions
Selmer groups
Class groups
Bernoulli-Carlitz numbers
topic Iwasawa Main Conjecture
Global function fields
L-functions
Selmer groups
Class groups
Bernoulli-Carlitz numbers
description We consider ZNp-extensions F of a global function field F and study various aspects of Iwasawa theory with emphasis on the two main themes already (and still) developed in the number fields case as well. When dealing with the Selmer group of an abelian variety A defined over F, we provide all the ingredients to formulate an Iwasawa Main Conjecture relating the Fitting ideal and the p-adic L-function associated to A and F. We do the same, with characteristic ideals and p-adic L-functions, in the case of class groups (using known results on characteristic ideals and Stickelberger elements for Zdp-extensions). The final section provides more details for the cyclotomic ZNp-extension arising from the torsion of the Carlitz module: in particular, we relate cyclotomic units with Bernoulli-Carlitz numbers by a Coates-Wiles homomorphism.
publishDate 2020
dc.date.none.fl_str_mv 2
2020-01-01
2020
2020-01-01
dc.type.none.fl_str_mv Capítol de llibre
http://purl.org/coar/resource_type/c_3248
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/bookPart
format bookPart
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/243142
https://dx.doi.org/urn:doi:10.4171/198-1/7
url https://ddd.uab.cat/record/243142
https://dx.doi.org/urn:doi:10.4171/198-1/7
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM2009-10359
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
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://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv European Mathematical Society Publishing House
publisher.none.fl_str_mv European Mathematical Society Publishing House
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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