Galois rigidity of pro- pure braid groups of algebraic curves
Galois rigidity of pro- pure braid groups of algebraic curves
复制标题
代数曲线预纯编织群的伽罗瓦刚性
DOI：
10.1090/s0002-9947-98-02038-8
复制
发表时间：
1998
影响因子：
1.3
通讯作者：
N. Takao
中科院分区：
文献类型：
--
作者：
Hiroaki Nakamura;N. Takao
本文将Grothendieck关于双曲曲线位形空间的亲基群的可倒猜想简化为关于单双曲曲线位形空间的可倒猜想。这是通过有效地估计曲线上的前- 1辫群的伽罗瓦等变自同构群来实现的。证明过程涉及到与黎曼曲面上编织群的权过滤相关的分级李代数的分级自同构群的完全确定。
In this paper, Grothendieck’s anabelian conjecture on the pro-l fundamental groups of configuration spaces of hyperbolic curves is reduced to the conjecture on those of single hyperbolic curves. This is done by estimating effectively the Galois equivariant automorphism group of the pro-l braid group on the curve. The process of the proof involves the complete determination of the groups of graded automorphisms of the graded Lie algebras associated to the weight filtration of the braid groups on Riemann surfaces.