代数几何中作为概形的万有覆盖空间与基本群
代数几何
2011-02-08 v4 代数拓扑
摘要
在拓扑学中，基本群与万有覆盖的概念紧密交织。通过将拓扑学中的通常概念引入代数和算术框架，我们从万有覆盖构造了一个基本群族，两者均为概形。基本群族（作为拓扑群）的一个几何纤维典范地是平展基本群。该构造适用于所有连通拟紧拟分离概形。在采用不同方法和假设的情况下，Deligne 已经构造了这一基本群族。
引用
@article{arxiv.0902.3464,
title = {Universal covering spaces and fundamental groups in algebraic geometry as schemes},
author = {Ravi Vakil and Kirsten Wickelgren},
journal= {arXiv preprint arXiv:0902.3464},
year = {2011}
}
备注
v2: Important references added. New example by David Harbater: the group scheme structure on the additive group does not lift to its universal cover in positive characteristic. v3: Article identical. arXiv abstract updated. v4: accepted version, J. Theor. Nombres Bordeaux, to appear