Fitting ideals of class groups in Carlitz-Hayes cyclotomic extensions

We generalize some results of Greither and Popescu to a geometric Galois cover X → Y which appears naturally for example in extensions generated by pn-torsion points of a rank 1 normalized Drinfeld module (i.e. in subextensions of Carlitz-Hayes cyclotomic extensions of global fields of positive char...

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Detalles Bibliográficos
Autores: Bandini, Andrea|||0000-0001-5876-348X, Bars Cortina, Francesc|||0000-0003-4779-3995, Coscelli, Edoardo|||0000-0002-7911-3854
Tipo de recurso: artículo
Fecha de publicación:2019
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:240659
Acceso en línea:https://ddd.uab.cat/record/240659
https://dx.doi.org/urn:doi:10.1016/j.jnt.2018.12.010
Access Level:acceso abierto
Palabra clave:Stickelberger series
L-functions
Class groups
Function fields
Carlitz-Hayes cyclotomic extensions
Descripción
Sumario:We generalize some results of Greither and Popescu to a geometric Galois cover X → Y which appears naturally for example in extensions generated by pn-torsion points of a rank 1 normalized Drinfeld module (i.e. in subextensions of Carlitz-Hayes cyclotomic extensions of global fields of positive characteristic). We obtain a description of the Fitting ideal of class groups (or of their dual) via a formula involving Stickelberger elements and providing a link (similar to the one in [1]) with Goss ζ-function.