Geometric version of the Grothendieck conjecture for universal curves over Hurwitz stacks

IF 0.4 4区 数学 Q4 MATHEMATICS
Shota Tsujimura
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引用次数: 0

Abstract

In this paper, we prove a certain geometric version of the Grothendieck Conjecture for tautological curves over Hurwitz stacks. This result generalizes a similar result obtained by Hoshi and Mochizuki in the case of tautological curves over moduli stacks of pointed smooth curves. In the process of studying this version of the Grothendieck Conjecture, we also examine various fundamental geometric properties of “profiled log Hurwitz stacks”, i.e., log algebraic stacks that parametrize Hurwitz coverings for which the marked points are equipped with a certain ordering determined by combinatorial data which we refer to as a “profile”.
赫维茨堆上普适曲线的几何版Grothendieck猜想
在本文中,我们证明了Hurwitz堆栈上重言曲线的Grothendieck猜想的一个几何版本。这一结果推广了Hoshi和Mochizuki在尖光滑曲线的模栈上的重言函数曲线的情况下获得的类似结果。在研究Grothendieck猜想的这个版本的过程中,我们还研究了“轮廓对数Hurwitz堆栈”的各种基本几何性质,即对Hurwitz覆盖进行参数化的对数代数堆栈,其标记点配备了由组合数据确定的特定阶序,我们称之为“轮廓”。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
0.90
自引率
0.00%
发文量
16
审稿时长
>12 weeks
期刊介绍: Kodai Mathematical Journal is edited by the Department of Mathematics, Tokyo Institute of Technology. The journal was issued from 1949 until 1977 as Kodai Mathematical Seminar Reports, and was renewed in 1978 under the present name. The journal is published three times yearly and includes original papers in mathematics.
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