Memoirs of the American Mathematical Society 2009; 81 pp; softcover Volume: 200 ISBN10: 0821844040 ISBN13: 9780821844045 List Price: US$65 Individual Members: US$39 Institutional Members: US$52 Order Code: MEMO/200/937
 This volume concerns invariants of \(G\)torsors with values in mod \(p\) Galois cohomologyin the sense of Serre's lectures in the book Cohomological invariants in Galois cohomologyfor various simple algebraic groups \(G\) and primes \(p\). The author determines 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. He also determines the invariants of \(\mathrm{Spin}_n\) mod 2 for \(n \leq 12\) and constructs some invariants of \(\mathrm{Spin}_{14}\). Along the way, the author proves that certain maps in nonabelian cohomology are surjective. These surjectivities give as corollaries Pfister's results on 10 and 12dimensional quadratic forms and Rost's theorem on 14dimensional quadratic forms. This material on quadratic forms and invariants of \(\mathrm{Spin}_n\) is based on unpublished work of Markus Rost. An appendix by Detlev Hoffmann proves a generalization of the Common Slot Theorem for 2Pfister quadratic forms. Table of Contents  Part I. Invariants, especially modulo an odd prime
 Part II. Surjectivities and invariants of \(E_6, E_7\), and \(E_8\)
 Part III. Spin groups
 Appendices
 Bibliography
 Index
