Newton Slopes for Artin-schreier-witt Towers
نویسندگان
چکیده
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 tower. We prove that, when the conductor of the character is large enough, the Newton slopes of the L-function form arithmetic progressions which are independent of the conductor of the character. As a corollary, we obtain a result on the behavior of the slopes of the eigencurve associated to the Artin-Schreier-Witt tower, analogous to the result of Buzzard and Kilford.
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 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.
متن کاملThe L-functions of Witt coverings
Results on L-functions of Artin-Schreier coverings by Dwork, Bombieri and AdolphsonSperber are generalized to L-functions of Witt coverings.
متن کاملSome Artin–schreier Towers Are Easy
Towers of function fields (resp., of algebraic curves) with positive limit provide examples of curves with large genus having many rational points over a finite field. It is in general a difficult task to calculate the genus of a wild tower. In this paper, we present a method for calculating the genus of certain Artin–Schreier towers. As an illustration of our method, we obtain a very simple an...
متن کاملSlope Estimates of Artin-schreier Curves
Let X/Fp be an Artin-Schreier curve defined by the affine equation yp−y = f̃(x) where f̃(x) ∈ Fp[x] is monic of degree d. In this paper we develop a method for estimating the first slope of the Newton polygon of X. Denote this first slope by NP1(X/Fp)). We use our method to prove that if p > d ≥ 2 then NP1(X/Fp) ≥ d p−1 d e p−1 . If p > 2d ≥ 4, we give a sufficient condition for the equality to h...
متن کامل