Universal covering spaces and fundamental groups in algebraic geometry as schemes
Publication
, Journal Article
Vakil, R; Wickelgren, K
Published in: Journal de Theorie des Nombres de Bordeaux
January 1, 2011
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.
Duke Scholars
Published In
Journal de Theorie des Nombres de Bordeaux
DOI
ISSN
1246-7405
Publication Date
January 1, 2011
Volume
23
Issue
2
Start / End Page
489 / 526
Related Subject Headings
- 4904 Pure mathematics
- 0101 Pure Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Vakil, R., & Wickelgren, K. (2011). Universal covering spaces and fundamental groups in algebraic geometry as schemes. Journal de Theorie Des Nombres de Bordeaux, 23(2), 489–526. https://doi.org/10.5802/jtnb.774
Vakil, R., and K. Wickelgren. “Universal covering spaces and fundamental groups in algebraic geometry as schemes.” Journal de Theorie Des Nombres de Bordeaux 23, no. 2 (January 1, 2011): 489–526. https://doi.org/10.5802/jtnb.774.
Vakil R, Wickelgren K. Universal covering spaces and fundamental groups in algebraic geometry as schemes. Journal de Theorie des Nombres de Bordeaux. 2011 Jan 1;23(2):489–526.
Vakil, R., and K. Wickelgren. “Universal covering spaces and fundamental groups in algebraic geometry as schemes.” Journal de Theorie Des Nombres de Bordeaux, vol. 23, no. 2, Jan. 2011, pp. 489–526. Scopus, doi:10.5802/jtnb.774.
Vakil R, Wickelgren K. Universal covering spaces and fundamental groups in algebraic geometry as schemes. Journal de Theorie des Nombres de Bordeaux. 2011 Jan 1;23(2):489–526.
Published In
Journal de Theorie des Nombres de Bordeaux
DOI
ISSN
1246-7405
Publication Date
January 1, 2011
Volume
23
Issue
2
Start / End Page
489 / 526
Related Subject Headings
- 4904 Pure mathematics
- 0101 Pure Mathematics