{"title":"Geometric version of the Grothendieck conjecture for universal curves over Hurwitz stacks","authors":"Shota Tsujimura","doi":"10.2996/kmj/kmj44305","DOIUrl":null,"url":null,"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”.","PeriodicalId":54747,"journal":{"name":"Kodai Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2021-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Kodai Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2996/kmj/kmj44305","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
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”.
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.