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Cohomological Invariants in Galois Cohomology

About this Title

Skip Garibaldi, Emory University, Atlanta, GA, Alexander Merkurjev, University of California, Los Angeles, Los Angeles, CA and Jean-Pierre Serre, Collège de France, Paris, France

Publication: University Lecture Series
Publication Year: 2003; Volume 28
ISBNs: 978-0-8218-3287-5 (print); 978-1-4704-2174-8 (online)
DOI: https://doi.org/10.1090/ulect/028
MathSciNet review: MR1999383
MSC: Primary 11E72; Secondary 12G05

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Table of Contents

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Front/Back Matter

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Cohomological invariants, Witt invariants, and trace forms

• Contents
• Introduction
• Chapter I. The notion of “invariant”
• Chapter II. Cohomological preliminaries: The local case
• Chapter III. Cohomological preliminaries: The function field case
• Chapter IV. Specialization properties of cohomological invariants
• Chapter V. Restriction and corestriction of invariants
• Chapter VI. Cohomological invariants of O$_n$, SO$_n$,…
• Chapter VII. Cohomological invariants of étale algebras
• Chapter VIII. Witt invariants
• Chapter IX. The trace form in dimension ${}\le 7$
• Appendix A. A letter from M. Rost to J-P. Serre
• Appendix B. A letter from J-P. Serre to R. S. Garibaldi
• Appendix C. A letter from B. Totaro to J-P. Serre

Rost invariants of simply connected algebraic groups

• Contents
• Rost invariants of simply connected algebraic groups
• Appendix A. The groups $H^{d+1}(F,\mathbb {Q}/\mathbb {Z}(d))$
• Appendix B. Tables of Dynkin indices