Cohomological Invariants (eBook)

Exceptional Groups and Spin Groups

Skip Garibaldi (Autor)

eBook Download: PDF

81 Seiten
American Mathematical Society (Verlag)
978-1-4704-0551-9 (ISBN)

Infos

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 $/mathrm{Spin}_n$ 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 12-dimensional quadratic forms and Rost's theorem on 14-dimensional 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 This material on quadratic forms and invariants of $/mathrm{Spin}_n$ is based on unpublished work of Markus Rost.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 2-Pfister quadratic forms.

Produkt-Details

• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• ISBN-10: 1-4704-0551-2 / 1470405512
• ISBN-13: 978-1-4704-0551-9 / 9781470405519