One-dimensional elementary-abelian extensions of local fields
نویسندگان
چکیده
The topology of an elementary abelian extension of local fields with one ramification break is, since there is only one break, rather symmetric with respect to Galois action. In this paper, we consider a particularly symmetric sub-class, which we call one-dimensional and in characteristic p is linked to the Artin-Schreier equation xp f −x = β. The utility of this additional symmetry is illustrated by an explicit description of Galois module structure.
منابع مشابه
One-dimensional Elementary Abelian Extensions Have Galois Scaffolding
Abstract. We define a variant of normal basis, called a Galois scaffolding, that allows for an easy determination of valuation, and has implications for Galois module structure. We identify fully ramified, elementary abelian extensions of local function fields of characteristic p, called one-dimensional, that, in a particular sense, are as simple as cyclic degree p extensions, and prove the sta...
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تاریخ انتشار 2008