Universal covering spaces and fundamental groups in algebraic geometry as schemes

Published

Journal Article

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 étale fundamental group. The constructions apply to all connected quasicompact quasiseparated schemes. With different methods and hypotheses, this fundamental group family was already constructed by Deligne. © Société Arithmétique de Bordeaux.

Full Text

Duke Authors

Cited Authors

  • Vakil, R; Wickelgren, K

Published Date

  • January 1, 2011

Published In

Volume / Issue

  • 23 / 2

Start / End Page

  • 489 - 526

International Standard Serial Number (ISSN)

  • 1246-7405

Digital Object Identifier (DOI)

  • 10.5802/jtnb.774

Citation Source

  • Scopus