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Cohomological Invariants: Exceptional Groups and Spin Groups
Skip Garibaldi, Emory University, Atlanta, GA
with an appendix by Detlev Hoffmann
cover
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Memoirs of the American Mathematical Society
2009; 81 pp; softcover
Volume: 200
ISBN-10: 0-8218-4404-0
ISBN-13: 978-0-8218-4404-5
List Price: US$65
Individual Members: US$39
Institutional Members: US$52
Order Code: MEMO/200/937
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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 This material on quadratic forms and invariants of \(\mathrm{Spin}_n\) is based on unpublished work of Markus Rost.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.

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
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