**Date & Time:** Monday, February 16, 2009, 16:00-17:00.

**Venue:** Room 216

**Title:** Abelian Galois Cohomology of Reductive Groups

**Speaker:** Mikhail Borovoi, Tel Aviv University

**Abstract:** For a connected reductive group *G* over a field *k* of characteristic *0*, we define a canonical and functorial map (the abelianization map) from the pointed set of the first Galois cohomology *H ^{1}(k,G)* into a certain abelian group (the group of abelian Galois cohomology). When

*k*is a

*p*-adic field or a totally imaginary number field, this abelianization map is bijective, hence

*H*has a canonical and functorial structure of an abelian group.

^{1}(k,G)