Local Galois module structure in positive characteristic and continued fractions

• Autores: Bart de Smit, Lara Thomas
• Localización: Archiv der Mathematik, ISSN 0003-889X, Vol. 88, Nº. 3, 2007, págs. 207-219
• Idioma: alemán
• DOI: 10.1007/s00013-006-1939-8
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• Resumen

  • 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.