## 2009 Topology Seminar - 15

- Date: 08/07/2009

Rick Jardine (University of Western Ontario)

University of British Columbia

Pointed torsors and Galois groups

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.

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