The ring of integers of Hopf-Galois degree p extensions of p-adic fields with dihedral normal closure

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10471944" target="_blank" >RIV/00216208:11320/23:10471944 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=IVhwdS34Uu" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=IVhwdS34Uu</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jnt.2022.10.002" target="_blank" >10.1016/j.jnt.2022.10.002</a>

Result language
angličtina
Original language name
The ring of integers of Hopf-Galois degree p extensions of p-adic fields with dihedral normal closure
Original language description
For an odd prime number p, we consider degree p extensions L/K of p-adic fields with normal closure Le such that the Galois group of Le/K is the dihedral group of order 2p. We shall prove a complete characterization of the freeness of the ring of integers OL over its associated order AL/K in the unique Hopf-Galois structure on L/K, which is analog to the one already known for cyclic degree p extensions of p-adic fields. We shall derive positive and negative results on criteria for the freeness of OL as AL/K-module.
Czech name
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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
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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