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Cohomological Invariants in Galois Cohomology
Skip Garibaldi, Emory University, Atlanta, GA, Alexander Merkurjev, University of California, Los Angeles, CA, and Jean-Pierre Serre, Collège de France, Paris, France
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University Lecture Series
2003; 168 pp; softcover
Volume: 28
ISBN-10: 0-8218-3287-5
ISBN-13: 978-0-8218-3287-5
List Price: US$39
Member Price: US$31.20
Order Code: ULECT/28
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This volume addresses algebraic invariants that occur in the confluence of several important areas of mathematics, including number theory, algebra, and arithmetic algebraic geometry. The invariants are analogues for Galois cohomology of the characteristic classes of topology, which have been extremely useful tools in both topology and geometry. It is hoped that these new invariants will prove similarly useful. Early versions of the invariants arose in the attempt to classify the quadratic forms over a given field.

The authors are well-known experts in the field. Serre, in particular, is recognized as both a superb mathematician and a master author. His book on Galois cohomology from the 1960s was fundamental to the development of the theory. Merkurjev, also an expert mathematician and author, co-wrote The Book of Involutions (Volume 44 in the AMS Colloquium Publications series), an important work that contains preliminary descriptions of some of the main results on invariants described here.

The book also includes letters between Serre and some of the principal developers of the theory. It will be of interest to graduate students and research mathematicians interested in number theory and Galois cohomology.

Readership

Graduate students and research mathematicians interested in number theory and Galois cohomology.

Table of Contents

Cohomological invariants, Witt invariants, and trace forms
  • J.-P. Serre and S. Garibaldi -- Contents
  • J.-P. Serre and S. Garibaldi -- Introduction
  • J.-P. Serre and S. Garibaldi -- The notion of "invariant"
  • J.-P. Serre and S. Garibaldi -- Cohomological preliminaries: The local case
  • J.-P. Serre and S. Garibaldi -- Cohomological preliminaries: The function field case
  • J.-P. Serre and S. Garibaldi -- Specialization properties of cohomological invariants
  • J.-P. Serre and S. Garibaldi -- Restriction and corestriction of invariants
  • J.-P. Serre and S. Garibaldi -- Cohomological invariants of \(O_n,SO_n,\ldots\)
  • J.-P. Serre and S. Garibaldi -- Cohomological invariants of étale algebras
  • J.-P. Serre and S. Garibaldi -- Witt invariants
  • J.-P. Serre and S. Garibaldi -- The trace form in dimension \(\le 7\)
  • M. Rost -- A letter from M. Rost to J-P. Serre
  • J.-P. Serre -- A letter from J-P. Serre to R. S. Garibaldi
  • B. Totaro -- A letter from B. Totaro to J-P. Serre
Rost invariants of simply connected algebraic groups
  • A. Merkurjev and S. Garibaldi -- Contents
  • A. Merkurjev and S. Garibaldi -- Rost invariants of simply connected algebraic groups
  • A. Merkurjev and S. Garibaldi -- The groups \(H^{d+1}(F,\mathbb{Q}/\mathbb{Z}(d))\)
  • A. Merkurjev and S. Garibaldi -- Tables of Dynkin indices
  • Bibliography
  • Index of notation
  • Index of terms
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