nLab
Chevalley fundamental group

Context

Homotopy theory

Group Theory

Contents

Idea

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.

References

Revised on September 1, 2014 08:01:21 by Urs Schreiber (82.113.98.44)