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...
| Autores: | , , |
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| 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 |
| 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. |
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