论文标题
Hurwitz树木和Artin-Schreier封面的变形
Hurwitz trees and deformations of Artin-Schreier covers
论文作者
论文摘要
让$ r $成为一个完全不同的特征$ p> 0 $的完整离散评估环。给定$ \ mathbb {z}/p $ -galois封面超过$ r $，一个人可以从中获得一个半稳定的模型，其分支点的特殊性是独特的，并且位于特殊光纤的平稳位置。该描述导致一个组合对象，该对象类似于混合特征的经典Hurwitz树，我们将给出相同的名称。 Hurwitz树的存在对于存在$ \ Mathbb {z}/p $ -cover的存在是必需的，其分支数据适合该树。我们表明，赫维兹树结构所施加的条件也足够了。使用此过程，我们改善了固定属的Artin-Schreier曲线模量空间的连接性。
Let $R$ be a complete discrete valuation ring of equal characteristic $p>0$. Given a $\mathbb{Z}/p$-Galois cover of a formal disc over $R$, one can derive from it a semi-stable model for which the specializations of branch points are distinct and lie in the smooth locus of the special fiber. The description leads to a combinatorial object which resembles a classical Hurwitz tree in mixed characteristic, which we will give the same name. The existence of a Hurwitz tree is necessary for the existence of a $\mathbb{Z}/p$-cover whose branching data fit into that tree. We show that the conditions imposed by a Hurwitz tree's structure are also sufficient. Using this, we improve a known result about the connectedness of the moduli space of Artin-Schreier curves of fixed genus.
