Galois rigidity of pure sphere braid groups and profinite calculus
Galois rigidity of pure sphere braid groups and profinite calculus
复制标题
纯球辫群的伽罗瓦刚度和有限微积分
DOI：
10.1090/s1056-3911-04-00376-5
复制
发表时间：
1994
影响因子：
--
通讯作者：
Hiroaki Nakamura
中科院分区：
文献类型：
--
作者：
Hiroaki Nakamura
设C是一类在子群、子群和群扩张的形式下闭的有限群。对于数域k上的代数簇X，设π C1（X）表示X的（C-修正的）pro-C基本群，其商为绝对Galois群Gal（<$k/k），核π C（X <$）为X的几何基本群的最大pro-C商.通过对π C 1（X）的外自同构群Outπ C（X）的研究，证明了π C（X）对双曲型X的刚性性质.特别是，委员会认为，
Let C be a class of finite groups closed under the for- mation of subgroups, quotients, and group extensions. For an algebraic variety X over a number field k, let π C 1 (X) denote the (C-modified) profi- nite fundamental group of X having the absolute Galois group Gal( ¯ k/k) as a quotient with kernel π C (X¯ ) the maximal pro-C quotient of the geo- metric fundamental group of X. The purpose of this paper is to show certain rigidity properties of π C (X) for X of hyperbolic type through the study of outer automorphism group Outπ C (X )o fπ C 1 (X). In particular,