Hopf-Galois module structure of quartic Galois extensions of Q
| Autor: | Daniel Gil-Muñoz, Anna Rio |
|---|---|
| Přispěvatelé: | Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. TN - Grup de Recerca en Teoria de Nombres |
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
Algebraic number theory
Algebra and Number Theory 11 Number theory::11R Algebraic number theory: global fields [Classificació AMS] Mathematics::Number Theory Nombres Teoria algebraica de Matemàtiques i estadística::Àlgebra [Àrees temàtiques de la UPC] Hopf-Galois structure Freeness over the associated order |
| Zdroj: | UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) |
| Popis: | © 2022 Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ Given a quartic Galois extension L/Q of number fields and a Hopf-Galois structure H on L/Q, we study the freeness of the ring of integers OL as module over the associated order AH in H. For the classical Galois structure Hc, we know by Leopoldt’s theorem that OL is AHc -free. If L/Q is cyclic, it admits a unique non-classical Hopf-Galois structure, whereas if it is biquadratic, it admits three such Hopf-Galois structures. In both cases, we obtain that freeness depends on the solvability in Z of certain generalized Pell equations. We shall translate some results on Pell equations into results on the AH-freeness of OL. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|