nLab Chevalley fundamental group



Homotopy theory

homotopy theory, (∞,1)-category theory, homotopy type theory

flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed

models: topological, simplicial, localic, …

see also algebraic topology



Paths and cylinders

Homotopy groups

Basic facts


Group Theory



The term Chevalley fundamental group is sometimes used for the fundamental group of a space defined via the automorphisms of a universal cover, hence its étale fundamental group (see there for more). In algebraic geometry/arithmetic geometry this is essentially the absolute Galois group

This terminology is used by Borceux and Janeldize in their book on Galois Theories. To quote from that source:

‘’ There are two classical definitions of the fundamental group of a topological space which give isomorphic groups for certain ‘’good’‘ spaces.“

The Chevalley fundamental group Aut(p)=Aut(E,p)Aut(p)= Aut(E,p) is defined only for connected spaces BB which admit a universal covering map p:EBp: E\to B with connected EE, and, of course, depends on it, but again, different pp produce isomorphic groups.’‘

The term algebraic fundamental group is also sometimes used for this, although more usually that term is reserved for Grothendieck’s fundamental group of a scheme.


Last revised on September 1, 2014 at 08:01:21. See the history of this page for a list of all contributions to it.