Iwasawa main conjecture for the Carlitz cyclotomic extension and applications
We prove an Iwasawa Main Conjecture for the class group of the p-cyclotomic extension F of the function field Fq(θ) (p is a prime of Fq[θ]), showing that its Fitting ideal is generated by a Stickelberger element. We use this and a link between the Stickelberger element and a p-adic L-function to pro...
| Autores: | , , , |
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| Formato: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:240658 |
| Acesso em linha: | https://ddd.uab.cat/record/240658 https://dx.doi.org/urn:doi:10.1007/s00208-019-01875-8 |
| Access Level: | acceso abierto |
| Palavra-chave: | Stickelberger series Carlitz-Goss ζ-function L-functions Bernoulli-Goss numbers Class groups Iwasawa Main Conjecture Function fields Cyclotomic extensions |
| Resumo: | We prove an Iwasawa Main Conjecture for the class group of the p-cyclotomic extension F of the function field Fq(θ) (p is a prime of Fq[θ]), showing that its Fitting ideal is generated by a Stickelberger element. We use this and a link between the Stickelberger element and a p-adic L-function to prove a close analog of the Ferrero-Washington Theorem for F and to provide information on the p-adic valuations of the Bernoulli-Goss numbers β(j) (i.e., on the values of the Carlitz-Goss ζ-function at negative integers). |
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