论文标题
关于非阿贝利安伊瓦川塔中的弗罗贝尼乌斯的变化
On the variation of the Frobenius in a non abelian Iwasawa tower
论文作者
论文摘要
对于有限字段$ \ mathbb f_q $的品种，带有“许多”自动形态，我们研究了Frobenius Operators of solology of frobenius eigenvalues的$ \ ell $ - adic属性。本文的主要目的是考虑诸如$ y^2 = f（x^{\ ell^n}）$之类的塔，并证明frobenius在典型的共同体中的特征多项式显示出令人惊讶的$ \ ell $ - ad-adic-adic contresgence。我们通过证明与偏斜的同一个同胞小组相关的某些不变性的融合的更一般性陈述来证明这一点。一路上，我们将证明许多天然序列$（x_n）_ {n \ geq 1} \ in \ mathbb z_ \ ell^{\ mathbb n} $ contionge $ \ ell $ thine $ thine $ - airtilly and-ofary $ thine $ - offical and-office and thince convergence。在不同的方向上，我们为曲线提供了一个精确的标准，这些曲线具有许多自动形态，具有超大型，概括和统一的许多旧结果。
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 $y^2 = f(x^{\ell^n})$ and prove that the characteristic polynomials of the Frobenius on the étale cohomology show a surprising $\ell$-adic convergence. We prove this by proving a more general statement about the convergence of certain invariants related to a skew-abelian cohomology group. Along the way, we will prove that many natural sequences $(x_n)_{n\geq 1} \in \mathbb Z_\ell^{\mathbb N}$ converge $\ell$-adically and give explicit rates of convergence. In a different direction, we provide a precise criterion for curves with many automorphisms to be supersingular, generalizing and unifying many old results.
