Arithmetic in generalized Artin-Schreier extensions of k(x)
نویسندگان
چکیده
منابع مشابه
Artin-schreier Extensions in Dependent and Simple Fields
We show that dependent elds have no Artin-Schreier extension, and that simple elds have only a nite number of them.
متن کاملRamification groups in Artin - Schreier - Witt extensions par Lara
Let K be a local field of characteristic p > 0. The aim of this paper is to describe the ramification groups for the prop abelian extensions over K with regards to the Artin-SchreierWitt theory. We shall carry out this investigation entirely in the usual framework of local class field theory. This leads to a certain non-degenerate pairing that we shall define in detail, generalizing in this way...
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 کاملPolars of Artin–schreier Curves
1. Introduction. In this paper we study some properties of the special family of Artin–Schreier curves related to the theory of polar curves we developed in [2]. Our goal is to show how this theory can be carried out in concrete situations and also show how it can be used to determine new upper bounds for the number of rational points of projective plane curves over finite fields. The method we...
متن کاملThe Two Artin-Schreier Theorems
Proof. We prove by the following steps: y 1 Start with induction on n, for n = 1 the result is trivial. y 2 Let g be such that σ1(g) ̸= σ2(g) and consider ∑ aiσi(gx) = 0 and ∑ aiσ1(g)σi(x) = 0 y 3 Cancel one summand by showing a2 = 0 and eventually show all ai = 0 One can prove by induction. Let a1σ1 ≡ 0 then since σ1 does not map to 0 ∈ K one must have a1 = 0. Suppose now that for any linear co...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1978
ISSN: 0022-314X
DOI: 10.1016/0022-314x(78)90027-6