论文标题
直到基本组的tht：构建基本组的标记同构 - 算术全态结构
Untilts of fundamental groups: construction of labeled isomorphs of fundamental groups -- Arithmetic Holomorphic Structures
论文作者
论文摘要
令$ p $为主要数字。令$ x/e $为有限扩展的几何连接，平滑，准标记的变体$ e/\ mathbb {q} _p $。在本文中，我证明存在$ x/e $的perpected（且因此也是典型的基本组）的存在，这些基本组由不同的算术全态结构标记，就像riemann surface $σ$的基本组的同源物一样。 $σ$的Teichmuller空间。这是[Joshi，2021a，b，c，2022]中阐述的理论的起点，本文旨在作为简短的草图和公告。此处介绍的算术塑形结构还提供了Shinichi Mochizuki在[Mochizuki，2021a，b，c，d]中使用的独特算术塑形结构。由于是否存在明显的算术问题。霍。 [Mochizuki，2021a，b，c，d]中的结构在[Scholze and Stix]中提出，我包括对[Scholze and Stix]的讨论。有关其他详细信息，请参见引言。
Let $p$ be a prime number. Let $X/E$ be a geometrically connected, smooth, quasi-projective variety over a finite extension $E/\mathbb{Q}_p$. In this paper I demonstrate the existence of isomorphs of the tempered (and hence also étale) fundamental group of $X/E$ which are labeled by distinct arithmetic holomorphic structures, just as isomorphs of the fundamental group of a Riemann surface $Σ$ may be labeled by Riemann surfaces (i.e. complex holomorphic structures) $Σ'$ in the Teichmuller space of $Σ$. This is the starting point of the theory elaborated in [Joshi, 2021a,b,c, 2022] for which this paper is intended as an brief sketch and announcement. Arithmetic holomorphic structures introduced here also provide distinct arithmetic holomorphic structures used by Shinichi Mochizuki in [Mochizuki,2021a,b,c,d]. Since the question of whether or not there exists distinct arith. hol. structures in [Mochizuki,2021a,b,c,d] was raised in [Scholze and Stix], I include a discussion of [Scholze and Stix]. See the introduction for additional details.
