Hopf-Galois module structure of quartic Galois extensions of Q

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10453502" target="_blank" >RIV/00216208:11320/22:10453502 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=d6lDcKmyfC" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=d6lDcKmyfC</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jpaa.2022.107045" target="_blank" >10.1016/j.jpaa.2022.107045</a>

Result language
angličtina
Original language name
Hopf-Galois module structure of quartic Galois extensions of Q
Original language description
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 %H in H. For the classical Galois structure Hc, we know by Leopoldt's theorem that OL is %Hc-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 %H-freeness of OL. (C) 2022 The Author(s). Published by Elsevier B.V.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GM21-00420M" target="_blank" >GM21-00420M: Universal Quadratic Forms and Class Numbers</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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