Artin-schreier Extensions in Dependent and Simple Fields
نویسندگان
چکیده
We show that dependent elds have no Artin-Schreier extension, and that simple elds have only a nite number of them.
منابع مشابه
A Note on the Schmid-witt Symbol and Higher Local Fields
For a local field of characteristic p > 0, K, the combination of local class field theory and Artin-Schreier-Witt theory yield what is known as the Schmid-Witt symbol. The symbol encodes interesting data about the ramification theory of p-extensions of K and we can, for example, use it to compute the higher ramification groups of such extensions. In 1936, Schmid discovered an explicit formula f...
متن کاملThe Artin-schreier Theorem
The algebraic closure of R is C, which is a finite extension. Are there other fields which are not algebraically closed but have an algebraic closure which is a finite extension? Yes. An example is the field of real algebraic numbers. Since complex conjugation is a field automorphism fixing Q, and the real and imaginary parts of a complex number can be computed using field operations and comple...
متن کاملar X iv : 0 90 6 . 46 26 v 1 [ m at h . N T ] 2 5 Ju n 20 09 THE GENUS FIELDS OF ARTIN - SCHREIER EXTENSIONS
Let q be a power of a prime number p. Let k = Fq(t) be the rational function field with constant field Fq. Let K = k(α) be an Artin-Schreier extension of k. In this paper, we explicitly describe the ambiguous ideal classes and the genus field of K . Using this result we study the p-part of the ideal class group of the integral closure of Fq[t] in K. And we also give an analogy of Rédei-Richadt’...
متن کاملOne-dimensional elementary-abelian extensions of local fields
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 illustra...
متن کاملWeil Descent Attack for Artin-Schreier Curves
In this paper, we show how the method introduced by Gaudry, Hess and Smart can be extended to a family of algebraic curves using Artin-Schreier extensions. This family also extends the number of hyperelliptic curves in characteristic 2 vulnarable to the Weil decent attack obtained by Galbraith. We also show that the genus of the resulting curve will be one of two easily computable values.
متن کامل