Universal covering spaces and fundamental groups in algebraic geometry as schemes

作者：Vakil Ravi^*; Wickelgren Kirsten

来源：Journal de Theorie des Nombres de Bordeaux, 2011, 23(2): 489-526.

In topology, the notions of the fundamental group and the universal cover are closely intertwined. By importing usual notions from topology into the algebraic and arithmetic setting, we construct a fundamental group family from a universal cover, both of which are schemes. A geometric fiber of the fundamental group family (as a, topological group) is canonically the etale fundamental group. The constructions apply to all connected quasi-compact quasiseparated schemes. With different methods and hypotheses, this fundamental group family was already constructed by Deligne.

• 出版日期2011