Factorisability and wildly ramified Galois extensions

David J. Burns

Annales de l'institut Fourier (1991)

  • Volume: 41, Issue: 2, page 393-430
  • ISSN: 0373-0956

Abstract

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Let L / K be an abelian extension of p -adic fields, and let 𝒪 denote the valuation ring of K . We study ideals of the valuation ring of L as integral representations of the Galois group Gal ( L / K ) . Assuming K is absolutely unramified we use techniques from the theory of factorisability to investigate which ideals are isomorphic to an 𝒪 -order in the group algebra K [ Gal ( l / K ) ] . We obtain several general and also explicit new results.

How to cite

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Burns, David J.. "Factorisability and wildly ramified Galois extensions." Annales de l'institut Fourier 41.2 (1991): 393-430. <http://eudml.org/doc/74923>.

@article{Burns1991,
abstract = {Let $L/K$ be an abelian extension of $p$-adic fields, and let $\{\cal O\}$ denote the valuation ring of $K$. We study ideals of the valuation ring of $L$ as integral representations of the Galois group $\{\rm Gal\}(L/K)$. Assuming $K$ is absolutely unramified we use techniques from the theory of factorisability to investigate which ideals are isomorphic to an $\{\cal O\}$-order in the group algebra $K[\{\rm Gal\}(l/K)]$. We obtain several general and also explicit new results.},
author = {Burns, David J.},
journal = {Annales de l'institut Fourier},
keywords = {ideals; valuation ring; integral representations; Galois group; factorisability},
language = {eng},
number = {2},
pages = {393-430},
publisher = {Association des Annales de l'Institut Fourier},
title = {Factorisability and wildly ramified Galois extensions},
url = {http://eudml.org/doc/74923},
volume = {41},
year = {1991},
}

TY - JOUR
AU - Burns, David J.
TI - Factorisability and wildly ramified Galois extensions
JO - Annales de l'institut Fourier
PY - 1991
PB - Association des Annales de l'Institut Fourier
VL - 41
IS - 2
SP - 393
EP - 430
AB - Let $L/K$ be an abelian extension of $p$-adic fields, and let ${\cal O}$ denote the valuation ring of $K$. We study ideals of the valuation ring of $L$ as integral representations of the Galois group ${\rm Gal}(L/K)$. Assuming $K$ is absolutely unramified we use techniques from the theory of factorisability to investigate which ideals are isomorphic to an ${\cal O}$-order in the group algebra $K[{\rm Gal}(l/K)]$. We obtain several general and also explicit new results.
LA - eng
KW - ideals; valuation ring; integral representations; Galois group; factorisability
UR - http://eudml.org/doc/74923
ER -

References

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