Lifting Artin–Schreier covers with maximal wild monodromy

Let k be an algebraically closed field of characteristic p > 0. We consider the problem of lifting p-cyclic covers of ${\mathbb{P}^{1}_k}$ as p-cyclic covers C of the projective line over some discrete valuation field K under the condition that the wild monodromy is maximal. We answer positively the problem for covers birationally given by w ^p ?w = t R(t) for any additive polynomial R(t). One gives further informations about the ramification filtration of the monodromy extension and in the case when p = 2, one computes the conductor exponent f (Jac(C)/K) and the Swan conductor sw(Jac(C)/K).     

Improvements of the Weil bound for Artin–Schreier curves

For the Artin–Schreier curve y ^q ? y = f(x) defined over a finite field \({{\mathbb F}_q}\) of q elements, the celebrated Weil bound for the number of \({{\mathbb F}_{q^r}}\)-rational points can be sharp, especially in super-singular cases and when r is divisible. In this paper, we show how the Weil bound can be significantly improved, using ideas from moment L-functions and Katz’s work on ?-adic monodromy calculations. Roughly speaking, we show that in favorable cases (which happens quite often), one can remove an extra \({\sqrt{q}}\) factor in the error term.     

Distribution of Artin–Schreier extensions

The article at hand contains exact asymptotic formulas for the distribution of conductors of elementary abelian p-extensions of global function fields of characteristic p. As a consequence for the distribution of discriminants, this leads to an exact asymptotic formula for simple cyclic extensions and an interesting lower bound for noncyclic elementary abelian extensions.     

Slope Estimates of Artin–Schreier Curves

Let X/F_p be an Artin–Schreier curve defined by the affine equation y ^p –y=f(x) where f(x)F_p[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/F_p). We use our method to prove that if p>d2 then NP₁(X/F_p)(p–1)/d/(p–1). If p>2d4, we give a sufficient condition for the equality to hold.     

Galois lines for the Artin–Schreier–Mumford curve

The arrangement of all Galois lines for the Artin–Schreier–Mumford curve in the projective 3-space is described. Surprisingly, there exist infinitely many Galois lines intersecting this curve.     

Artin–Schreier extensions of the rational function field

In this paper we study the arithmetic of Artin–Schreier extensions of $\mathbb {F}_{q}(T)$ . We determine the integral closure of $\mathbb {F}_{q}[T]$ in Artin–Schreier extension of $\mathbb {F}_{q}(T)$ . We also investigate the average values of the $L$ -functions of orders of Artin–Schreier extensions and study the average values of ideal class numbers when $p=3$ in detail.     

Igusa–Todorov functions for Artin algebras

In this paper we study the behavior of the Igusa–Todorov functions for Artin algebras A with finite injective dimension, and Gorenstein algebras as a particular case. We show that the ?-dimension and ψ-dimension are finite in both cases. Also we prove that monomial, gentle and cluster tilted algebras have finite ?-dimension and finite ψ-dimension.     

On the distribution of zeroes of Artin–Schreier L-functions

We study the distribution of the zeroes of the L-functions of curves in the Artin–Schreier family. We consider the number of zeroes in short intervals and obtain partial results which agree with a random unitary matrix model.     

Gagliardo–Nirenberg inequality for maximal functions measuring smoothness

We prove a Galiardo–Nirenberg type pointwise interpolation inequality for special maximal functions which measure smoothness in the multidimensional case. It turns out that the classsical inequality follows from this one; it is also possible to use naturally BMO norms in the inequality. Bibliography: 6 titles.     

Multisequences with large linear and k-error linear complexity from a tower of Artin–Schreier extensions of function fields

In this paper, we construct multisequences with both large (joint) linear complexity and k-error (joint) linear complexity from a tower of Artin–Schreier extensions of function fields. Moreover, these sequences can be explicitly constructed.