论文标题
拓扑空间的亲代基本组
A pro-algebraic fundamental group for topological spaces
论文作者
论文摘要
考虑一个连接的拓扑空间$ x $，x $中的点$ x \，让$ k $成为具有离散拓扑的字段。我们研究了$ x $上的有限尺寸（Flat）向量捆绑包的Tannakian类别，其Tannakian Dual $π_k（x，x，x）$相对于$ x $。 $π_k（x，x）$的最大支持者是由kucharczyk和scholze研究的$ x $的基本组。对于表现良好的拓扑空间，$π_k（x，x）$是普通基本组$π_1（x，x）$的亲代代数完成。 我们通过研究（伪 - ）托架附加在其商中的$π_k（x，x）$上获得了一些结构性结果。这种方法在代数几何形状中使用了诺里的思想，并在坦纳基人类别上使用了deLigne的结果。我们还为某些广义螺线管计算$π_K（x，x）$。
Consider a connected topological space $X$ with a point $x \in X$ and let $K$ be a field with the discrete topology. We study the Tannakian category of finite dimensional (flat) vector bundles on $X$ and its Tannakian dual $π_K (X,x)$ with respect to the fibre functor in $x$. The maximal pro-étale quotient of $π_K (X,x)$ is the étale fundamental group of $X$ studied by Kucharczyk and Scholze. For well behaved topological spaces, $π_K (X,x)$ is the pro-algebraic completion of the ordinary fundamental group $π_1 (X,x)$. We obtain some structural results on $π_K (X,x)$ by studying (pseudo-)torsors attached to its quotients. This approach uses ideas of Nori in algebraic geometry and a result of Deligne on Tannakian categories. We also calculate $π_K (X,x)$ for some generalized solenoids.
