Homotopy groups of spectra and p-adic L-functions over number fields
(English) The goal of this thesis has been to represent the p-adic valuation of the special values of p-adic L-functions via Euler Characteristics using different cohomology theories in various settings. More specifically, homotopy theoretic invariants such as the K(1)-local K-theory spectrum have b...
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| Tipo de recurso: | tesis doctoral |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/452517 |
| Acceso en línea: | https://hdl.handle.net/2117/452517 https://dx.doi.org/10.5821/dissertation-2117-452517 |
| Access Level: | acceso abierto |
| Palabra clave: | 51 - Matemàtiques Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | (English) The goal of this thesis has been to represent the p-adic valuation of the special values of p-adic L-functions via Euler Characteristics using different cohomology theories in various settings. More specifically, homotopy theoretic invariants such as the K(1)-local K-theory spectrum have been used to describe these values in the setting of commutative and noncommutative totally real fields and also in some cases for imaginary quadratic fields. The most successful case has been in the commutative and totally real case, where the padic valuation of the Deligne-Ribet p-adic L-function can now be understood using étale cohomology, K(1)-local K-theory, and also as the fiber of the (K(1)-local) cyclotomic trace map, therefore extending the work of Hesselholt, which only covered F = Q. In addition to this, the foundation has been layed to extend these results in other directions, such as in the case of function fields, or more precisely, to the case of Abelian varieties with semistable reduction over function fields. |
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