Cohomological Invariants: Exceptional Groups and Spin Groups

This volume concerns invariants of G-torsors with values in mod p Galois cohomology - in the sense of Serre's lectures in the book Cohomological invariants in Galois cohomology - for various simple algebraic groups G and primes p. We determine the invariants for the exceptional groups F-4 mod 3, simply connected E-6 mod 3, E-7 mod 3, and E-8 mod 5. We also determine the invariants of Spin,, mod 2 for n <= 12 and construct some invariants of Spin(14). Along the way, we prove that certain maps in nonabelian cohomology are surjective. These surjectivities give as corollaries Pfister's results on 10- and 12-dimensional quadratic forms and Rost's theorem on 14-diniensional quadratic forms. This material on quadratic forms and invariants of Spin,, is based on unpublished work of Markus Rost. An appendix by Detlev Hoffmann proves a generalization of the Common Slot Theorem for 2-Pfister quadratic forms.