2009/02/19 by Ravi Vakil, Vakil, Ravi, Kirsten Wickelgren +1
Mathematics · #14F20 (Secondary) #14F30 (Primary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.0902.3464
openalex publication_date 2009/02/19 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
In topology, the notions of the fundamental group and the universal cover are\nclosely intertwined. By importing usual notions from topology into the\nalgebraic and arithmetic setting, we construct a fundamental group family from\na universal cover, both of which are schemes. A geometric fiber of the\nfundamental group family (as a topological group) is canonically the 'etale\nfundamental group. The constructions apply to all connected quasicompact\nquasiseparated schemes. With different methods and hypotheses, this fundamental\ngroup family was already constructed by Deligne.\n