Cohomological Invariants Exceptional Groups and Spin Groups is popular PDF and ePub book, written by Skip Garibaldi in 2009-06-05, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Cohomological Invariants Exceptional Groups and Spin Groups can be Read Online from any device for your convenience.
Cohomological Invariants Exceptional Groups and Spin Groups Book PDF Summary
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 This material on quadratic forms and invariants of $\mathrm{Spin}_n$ is based on unpublished work of Markus Rost.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.
Detail Book of Cohomological Invariants Exceptional Groups and Spin Groups PDF
- Author : Skip Garibaldi
- Release : 05 June 2009
- Publisher : American Mathematical Soc.
- ISBN : 9780821844045
- Genre : Mathematics
- Total Page : 102 pages
- Language : English
- PDF File Size : 21,7 Mb
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