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Archiv der Mathematik

, Volume 88, Issue 3, pp 207–219 | Cite as

Local Galois module structure in positive characteristic and continued fractions

  • Bart de SmitEmail author
  • Lara Thomas
Open Access
Article

Abstract.

For a Galois extension of degree p of local fields of characteristic p, we express the Galois action on the ring of integers in terms of a combinatorial object: a balanced {0, 1}-valued sequence that only depends on the discriminant and p. We show that the embedding dimension edim(R) of the associated order R is tightly related to the minimal number d of R-module generators of the ring of integers. Moreover, we show how to compute d and edim(R) from p and the discriminant with a continued fraction expansion.

Mathematics Subject Classification (2000).

Primary: 11R33 Secondary: 11J70, 68R15 

Keywords.

Galois module structure local fields Artin-Schreier extensions associated orders embedding dimension continued fractions 

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  1. 1.Mathematisch InstituutUniversiteit LeidenLeidenNetherlands
  2. 2.Chaire de Structures Algébriques et GéométriquesEcole Polytechnique Fédérale de LausanneLausanneSwitzerland

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