Artin-Schreier theory for commutative regular rings
نویسندگان
چکیده
منابع مشابه
The 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...
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We fix a monic polynomial f(x) ∈ Fq[x] over a finite field and consider the Artin-Schreier-Witt tower defined by f(x); this is a tower of curves · · · → Cm → Cm−1 → · · · → C0 = A, with total Galois group Zp. We study the Newton slopes of zeta functions of this tower of curves. This reduces to the study of the Newton slopes of L-functions associated to characters of the Galois group of this tow...
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...
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Lachaud, G., Artin-Schreier curves, exponential sums, and coding theory, Theoretical Computer Science 94 (1992) 295-310. This is a survey of some results recently obtained on the distribution of the weights of some classical linear codes on the one hand, such as the dual of the Melas code, and the geometric BCH codes discovered by Goppa (subfield subcodes of Goppa codes) on the other hand. Thes...
متن کاملIsomorphisms between Artin-Schreier towers
We give a method for efficiently computing isomorphisms between towers of Artin-Schreier extensions over a finite field. We find that isomorphisms between towers of degree pn over a fixed field Fq can be computed, composed, and inverted in time essentially linear in pn. The method relies on an approximation process.
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ژورنال
عنوان ژورنال: Annals of Mathematical Logic
سال: 1977
ISSN: 0003-4843
DOI: 10.1016/0003-4843(77)90012-2