论文标题
刺穿光谱基本群体的有限发电量的有限生成
Finite generation of nilpotent quotients of fundamental groups of punctured spectra
论文作者
论文摘要
在SGA 2中，Grothendieck的猜想认为，完整的Noetherian局部维度域的典型谱系的基本组至少两个具有代数封闭的残留场是拓扑结构的。在本文中，我们证明了一个较弱的陈述，即，基本组的最大亲态商在拓扑上是有限生成的。该证明使用$ p $ - adic附近的周期和相交配对的负面确定性对奇异性的分辨率以及对变形共同体某些代数组结构的谎言代数分析的某些分析。
In SGA 2, Grothendieck conjectures that the étale fundamental group of the punctured spectrum of a complete noetherian local domain of dimension at least two with algebraically closed residue field is topologically finitely generated. In this paper, we prove a weaker statement, namely that the maximal pro-nilpotent quotient of the fundamental group is topologically finitely generated. The proof uses $p$-adic nearby cycles and negative definiteness of intersection pairings over resolutions of singularities as well as some analysis of Lie algebras of certain algebraic group structures on deformation cohomology.
