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.
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We thank Bruno Anglès, Wieb Bosma and Rob Tijdeman for their bibliographic assistance.
Received: 19 March 2006
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de Smit, B., Thomas, L. Local Galois module structure in positive characteristic and continued fractions. Arch. Math. 88, 207–219 (2007). https://doi.org/10.1007/s00013-006-1939-8
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DOI: https://doi.org/10.1007/s00013-006-1939-8