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...
| Autores: | , , |
|---|---|
| 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 |
| Sumario: | 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. |
|---|