Tame Anabelian Geometry and Moduli Spaces of Curves over Algebraically Closed Fields of Characteristic p > 0
Tame Anabelian Geometry and Moduli Spaces of Curves over Algebraically Closed Fields of Characteristic p > 0
复制标题
驯服阿纳贝尔几何和代数闭特征域上的曲线模空间 p > 0
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Yu Yang
中科院分区：
文献类型：
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作者：
Yu Yang
本文研究了正特征曲线的驯服的Anabel几何。设（Xi，DXi），i ∈ {1，2}是特征p > 0的代数闭域ki上的（gX，nX）型光滑点稳定曲线，π t1（UXi）是UXi的驯服基本群def = Xi \ DXi .证明了：若gX = 0，k1 = k2 = Fp是Fp的代数闭包，则UX 1与UX 2作为概型同构当且仅当π t1（UX 1）与π t1（UX 2）之间存在开连续同态.这个结果推广了A.玉川本文从模空间的观点给出了特征p > 0的代数闭域上曲线的驯服基本群的一些新的性质。这些新的猜想是由Tamagawa提出的关于特征p > 0的代数闭域上曲线的Grothendieck猜想的弱Isom版本（=弱Isom版本猜想）的推广版本。此外，新的定理还阐明了模空间的拓扑结构与驯服基本群的开连续同态集之间的关系，以及Fp上的弱同构猜想与特征p > 0的任意代数闭域上的弱同构猜想之间的关系.
In the present paper, we study the tame anabelian geometry of curves in positive characteristic. Let (Xi, DXi), i ∈ {1, 2}, be a smooth pointed stable curve of type (gX , nX) over an algebraically closed field ki of characteristic p > 0 and π t 1(UXi) the tame fundamental group of UXi def = Xi \ DXi . We prove that, if gX = 0 and k1 = k2 = Fp is an algebraic closure of Fp, then UX1 is isomorphic to UX2 as schemes if and only if there exists an open continuous homomorphism between πt 1(UX1) and πt 1(UX2). This result generalizes the weak Isom-version of the Grothendieck conjecture for curves of type (0, nX) over Fp which has been proven by A. Tamagawa. We formulate some new conjectures concerning tame fundamental groups of curves over algebraically closed fields of characteristic p > 0 from the point of view of moduli spaces. The new conjectures are generalized versions of the weak Isom-version of the Grothendieck conjecture for curves over algebraically closed fields of characteristic p > 0 (=Weak Isom-version Conjecture) which was formulated by Tamagawa. Moreover, the new conjectures make clear the relationship between topological structures of moduli spaces and sets of open continuous homomorphisms of tame fundamental groups of curves, and the relationship between Weak Isom-version Conjecture over Fp and Weak Isom-version Conjecture over arbitrary algebraically closed fields of characteristic p > 0.
DOI：
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发表时间：
2008
期刊：
J. Math. Kyoto Univ. 47
影响因子：
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作者：
Eyral;C;Oka;M.;倉田 俊彦;R.Kobayashi;A.Hiraki and J.Koolen;望月新一
通讯作者：
望月新一
关于节点非简并外表示的组合阿贝尔几何
DOI：
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发表时间：
2011
期刊：
Hiroshima Math.J.
影响因子：
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作者：
Y.Hoshi;S.Mochizuki
通讯作者：
S.Mochizuki
具有规定基本群的正特征曲线同构类的有限性。
DOI：
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发表时间：
2004
期刊：
J. Algebraic Geom 13, no.4
影响因子：
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作者：
Ohyama;Y.;et. al.;A.Tamagawa
通讯作者：
A.Tamagawa