2009 Topology Seminar - 15

• Date: 08/07/2009
Lecturer(s):

Rick Jardine (University of Western Ontario)

Location:

University of British Columbia

Topic:

Pointed torsors and Galois groups

Description:

Suppose that H is an algebraic group which is defined over a field k,
and let L be the algebraic closure of k. The canonical stalk for the
etale topology on k induces a simplicial set map from the classifying
space B(H-tors) of the groupoid of H-torsors (aka. principal H-bundles)
to the space BH(L). The homotopy fibres of this map are groupoids of
pointed torsors, suitably defined. These fibres can be analyzed with
cocycle techniques: their path components are representations of the
"absolute Galois groupoid" in H, and each path component is
contractible. The arguments for these results are relatively simple,
and applications will be displayed.

Schedule:

3:00pm-4:00pm, WMAX 216