Cohomological Invariants: Exceptional Groups and Spin Groups

Released on by Skip Garibaldi
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  • Cohomological Invariants: Exceptional Groups and Spin Groups Book Detail

  • Author : Skip Garibaldi
  • Release Date : 2009-06-05
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 102
  • ISBN 13 : 0821844040
  • File Size : 8,8 MB
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Cohomological Invariants: Exceptional Groups and Spin Groups by Skip Garibaldi PDF Summary

Book Description: 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 This material on quadratic forms and invariants of $\mathrm{Spin}_n$ is based on unpublished work of Markus Rost.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.

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Algebraic Groups: Structure and Actions

Algebraic Groups: Structure and Actions

File Size : 77,77 MB
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This volume contains the proceedings of the 2015 Clifford Lectures on Algebraic Groups: Structures and Actions, held from March 2–5, 2015, at Tulane Universit