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 $p$. 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 $\textrm{Spin}_n$ mod 2 for $n \leq 12$ and constructs some invariants of $\textrm{Spin}_{14}$.

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 12-dimensional quadratic forms and Rost's theorem on 14-dimensional quadratic forms. This material on quadratic forms and invariants of $\textrm{Spin}_n$ is based on unpublished work of Markus Rost.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.

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