Galois module structure of ideals in wildly ramified cyclic extensions of degree p 2

Gove Griffith Elder

Annales de l'institut Fourier (1995)

  • Volume: 45, Issue: 3, page 625-647
  • ISSN: 0373-0956

Abstract

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For L / K , any totally ramified cyclic extension of degree p 2 of local fields which are finite extensions of the field of p -adic numbers, we describe the ℤ p [ Gal ( L / K ) ] -module structure of each fractional ideal of L explicitly in terms of the 4 p + 1 indecomposable ℤ p [ Gal ( L / K ) ] -modules classified by Heller and Reiner. The exponents are determined only by the invariants of ramification.

How to cite

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Elder, Gove Griffith. "Galois module structure of ideals in wildly ramified cyclic extensions of degree $p^2$." Annales de l'institut Fourier 45.3 (1995): 625-647. <http://eudml.org/doc/75132>.

@article{Elder1995,
abstract = {For $L/K$, any totally ramified cyclic extension of degree $p^2$ of local fields which are finite extensions of the field of $p$-adic numbers, we describe the $\{\Bbb Z\}_p[\{\rm Gal\}(L/K)]$-module structure of each fractional ideal of $L$ explicitly in terms of the $4p+1$ indecomposable $\{\Bbb Z\}_p[\{\rm Gal\}(L/K)]$-modules classified by Heller and Reiner. The exponents are determined only by the invariants of ramification.},
author = {Elder, Gove Griffith},
journal = {Annales de l'institut Fourier},
keywords = {Galois module structure; wild ramification; local number field; integral representation; finite representation type},
language = {eng},
number = {3},
pages = {625-647},
publisher = {Association des Annales de l'Institut Fourier},
title = {Galois module structure of ideals in wildly ramified cyclic extensions of degree $p^2$},
url = {http://eudml.org/doc/75132},
volume = {45},
year = {1995},
}

TY - JOUR
AU - Elder, Gove Griffith
TI - Galois module structure of ideals in wildly ramified cyclic extensions of degree $p^2$
JO - Annales de l'institut Fourier
PY - 1995
PB - Association des Annales de l'Institut Fourier
VL - 45
IS - 3
SP - 625
EP - 647
AB - For $L/K$, any totally ramified cyclic extension of degree $p^2$ of local fields which are finite extensions of the field of $p$-adic numbers, we describe the ${\Bbb Z}_p[{\rm Gal}(L/K)]$-module structure of each fractional ideal of $L$ explicitly in terms of the $4p+1$ indecomposable ${\Bbb Z}_p[{\rm Gal}(L/K)]$-modules classified by Heller and Reiner. The exponents are determined only by the invariants of ramification.
LA - eng
KW - Galois module structure; wild ramification; local number field; integral representation; finite representation type
UR - http://eudml.org/doc/75132
ER -

References

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