Skip Garibaldi

Applications of motives to Galois cohomology of algebraic groups

Abstract: When studying Galois cohomology of semisimple algebraic groups, one often wants to know the fibers of some cohomological invariant.  One well-known solution to this kind of problem is Merkurjev's Theorem saying that every quadratic form in $I^2$ with trivial Clifford invariant actually belongs to $I^3$.  We describe analogous results for exceptional groups, all proved using motivic techniques but with no motives appearing in the statements.