How far is an extension of p-adic fields from having a normal integral basis?
| Autor: | Davide Lombardo, Ilaria Del Corso, Fabio Ferri |
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| Rok vydání: | 2022 |
| Předmět: |
p-adic fields
Pure mathematics Algebra and Number Theory Mathematics - Number Theory Degree (graph theory) Group (mathematics) Mathematics::Number Theory Galois module structure Basis (universal algebra) Extension (predicate logic) Rings of integers Ramification FOS: Mathematics Number Theory (math.NT) Galois extension Normal integral bases Mathematics::Representation Theory Mathematics |
| Zdroj: | Journal of Number Theory. 233:158-197 |
| ISSN: | 0022-314X |
| DOI: | 10.1016/j.jnt.2021.06.008 |
| Popis: | Let $L/K$ be a finite Galois extension of $p$-adic fields with group $G$. It is well-known that $\mathcal{O}_L$ contains a free $\mathcal{O}_K[G]$-submodule of finite index. We study the minimal index of such a free submodule, and determine it exactly in several cases, including for any cyclic extension of degree $p$ of $p$-adic fields. 31 pages. v2: minor typos corrected (a factor 1/2 was missing in the statement of Proposition 3.5), results unchanged |
| Databáze: | OpenAIRE |
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