Related papers: Newton slopes for Artin-Schreier-Witt towers

We fix a monic polynomial $\bar f(x) \in \mathbb{F}_q[x]$ over a finite field of characteristic $p$, and consider the $\mathbb{Z}_{p^{\ell}}$-Artin-Schreier-Witt tower defined by $\bar f(x)$; this is a tower of curves $\cdots \to C_m \to…

Any polynomial $f(x)\in\mathbb{Z}_q[x]$ defines a Witt vector $[f]\in W(\mathbb{F}_q[x])$. Consider the Artin-Schreier-Witt tower $y^F-y=[f]$. This is a tower of curves over $\mathbb{F}_q$, with total Galois group $\mathbb{Z}_p$. We want to…

We fix a monic polynomial $f(x) \in \mathbb F_q[x]$ over a finite field of characteristic $p$ of degree relatively prime to $p$. Let $a\mapsto \omega(a)$ be the Teichm\"uller lift of $\mathbb F_q$, and let $\chi:\mathbb{Z}\to \mathbb…

We prove that for any generic polynomial $f$ in two variables of degree $(d_1,d_2)$ over the rationals, for $p$ large enough the Newton slopes of the character power series $C_f^*(\chi_m,s)$ of $f$ at $p$ is independent of the choice of the…

In this article we study the behavior of Newton polygons along $\mathbb{Z}_p$-towers of curves. Fix an ordinary curve $X$ over a finite field $\mathbb{F}_q$ of characteristic $p$. By a $\mathbb{Z}_p$-tower $X_\infty/X$ we mean a tower of…

Let $p$ be a prime number. Every $n$-variable polynomial $f(\underline x)$ over a finite field of characteristic $p$ defines an Artin--Schreier--Witt tower of varieties whose Galois group is isomorphic to $\mathbb{Z}_p$. Our goal of this…

Let $p$ be a prime number. Every two-variable polynomial $f(x_1, x_2)$ over a finite field of characteristic $p$ defines an Artin--Schreier--Witt tower of surfaces whose Galois group is isomorphic to $\mathbb Z_p$. Our goal of this paper is…

An Artin-Schreier tower over the finite field F_p is a tower of field extensions generated by polynomials of the form X^p - X - a. Following Cantor and Couveignes, we give algorithms with quasi-linear time complexity for arithmetic…

Let $K$ be a function field over a finite field $k$ of characteristic $p$ and let $K_{\infty}/K$ be a geometric extension with Galois group $\mathbb{Z}_p$. Let $K_n$ be the corresponding subextension with Galois group…

Let f(x) = x^d + a_{d-1}x^{d-1} + ... + a_0 be a polynomial of degree d in Q[x]. For every prime number p coprime to d and f(x) in (Z_p \cap Q)[x], let X/F_p be the Artin-Schreier curve defined by the affine equation y^p - y = f(x) mod p.…

To understand L-function is an important fundamental question in Number Theory, but there are few specific results on it, especially the calculation of its Newton polygon. Following Dwork's method it is hard to calculate an exact example,…

Given a prime number $p$, we consider the tower of finite fields $F_p=L_{-1}\subset L_0\subset L_1\subset\cdots$, where each step corresponds to an Artin-Schreier extension of degree $p$, so that for $i\geq 0$, $L_{i}=L_{i-1}[c_{i}]$, where…

We provide first slope estimates of the Newton polygon of generalized Artin-Schreier curves, which are proved using the action of Frobenius and Verschiebung on cohomology. We provide a number of applications such as an improved Hasse-Weil…

For varieties over a finite field $\mathbb F_q$ with "many" automorphisms, we study the $\ell$-adic properties of the eigenvalues of the Frobenius operator on their cohomology. The main goal of this paper is to consider towers such as $y^2…

Sect 1 introduces Nielsen classes attached to (G,C), where C is r conjugacy classes in a finite group G, and a braid action on them. These give reduced Hurwitz spaces, denoted H(G,C)^rd. The section concludes with a braid formula for the…

For prime $p\equiv-1\bmod d$ and $q$ a power of $p$, we obtain the slopes of the $q$-adic Newton polygons of $L$-functions of $x^d+ax^{d-1}\in \mathbb{F}_q[x]$ with respect to finite characters $\chi$ when $p$ is larger than an explicit…

We prove a finiteness result for the p-adic cohomology of the Lubin-Tate tower. For any n>=1 and p-adic field F, this provides a canonical functor from admissible p-adic representations of GL_n(F) towards admissible p-adic representations…

Let k be an algebraically closed field of characteristic p > 0. Every Artin-Schreier k-curve X has an equation of the form y^p - y = f(x) for some f(x) in k(x) such that p does not divide the least common multiple L of the orders of the…

In this paper we construct a Dwork theory for general exponential sums over affinoids in Witt towers. Using this, we compute the degree of the $L$-function, its Hodge polygon and examine when the Hodge and Newton polygons coincide.

We study the geometry of Bott towers in the context of toric geometry, describing their associated fans arising from crosspolytopes. We compute the cohomology ring of each stage of the tower, and provide all monomial identities defining…