with an appendix by Detlev Hoffmann
| eBook ISBN: | 978-1-4704-0551-9 |
| Product Code: | MEMO/200/937.E |
| List Price: | $69.00 |
| MAA Member Price: | $62.10 |
| AMS Member Price: | $41.40 |
with an appendix by Detlev Hoffmann
| eBook ISBN: | 978-1-4704-0551-9 |
| Product Code: | MEMO/200/937.E |
| List Price: | $69.00 |
| MAA Member Price: | $62.10 |
| AMS Member Price: | $41.40 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 200; 2009; 81 ppMSC: Primary 11; Secondary 12; 20; 17
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 This material on quadratic forms and invariants of \(\mathrm{Spin}_n\) is based on unpublished work of Markus Rost.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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Table of Contents
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Chapters
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Preface
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Part I. Invariants, especially modulo an odd prime
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Part II. Surjectivities and invariants of $E_6$, $E_7$, and $E_8$
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Part III. Spin groups
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Appendices
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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.
-
Chapters
-
Preface
-
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
