Group-theoretic characterizations of almost open immersions of curves

JOURNAL OF ALGEBRA

卷:530

Article

Yang, Yu¹ 

[1] Kyoto Univ, Res Inst Math Sci, Kyoto 6068502, Japan

关键词: Hyperbolic curve;    Fundamental group;    Anabelian geometry;   

DOI  :  10.1016/j.jalgebra.2019.04.016

来源: Elsevier

【 摘 要 】

Let p be a prime number and k either a finite field of characteristic p or a generalized sub-p-adic field. Let X-1 and X-2 be hyperbolic curves over k. In the present paper, we introduce a kind of morphism between X-1 and X-2 called an almost open immersion, and give some group-theoretic an almost open immersion, and give some group-theoretic characterizations for the set of almost open immersions between X-1 and X-2 via their arithmetic fundamental groups. This result generalizes the Isom-version of Grothendieck's anabelian conjecture for curves over k which has been proven by S. Mochizuki and A. Tamagawa to the case of almost open immersions. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free