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.
Reihe
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Illustrationen
bibliography, tables, index
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ISBN-13
978-0-8218-3287-5 (9780821832875)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
(College de France, Paris, France)
Cohomological invariants, Witt invariants, and trace forms: Contents by J.-P. Serre and S. Garibaldi Introduction by J.-P. Serre and S. Garibaldi The notion of "invariant" by J.-P. Serre and S. Garibaldi Cohomological preliminaries: The local case by J.-P. Serre and S. Garibaldi Cohomological preliminaries: The function field case by J.-P. Serre and S. Garibaldi Specialization properties of cohomological invariants by J.-P. Serre and S. Garibaldi Restriction and corestriction of invariants by J.-P. Serre and S. Garibaldi Cohomological invariants of $O_n,SO_n,\ldots$ by J.-P. Serre and S. Garibaldi Cohomological invariants of etale algebras by J.-P. Serre and S. Garibaldi Witt invariants by J.-P. Serre and S. Garibaldi The trace form in dimension $\le 7$ by J.-P. Serre and S. Garibaldi A letter from M. Rost to J-P. Serre by M. Rost A letter from J-P. Serre to R. S. Garibaldi by J.-P. Serre A letter from B. Totaro to J-P. Serre by B. Totaro Rost invariants of simply connected algebraic groups: Contents by A. Merkurjev and S. Garibaldi Rost invariants of simply connected algebraic groups by A. Merkurjev and S. Garibaldi The groups $H^{d+1}(F,\mathbb{Q}^mathbb{Z}(d))$ by A. Merkurjev and S. Garibaldi Tables of Dynkin indices by A. Merkurjev and S. Garibaldi Bibliography Index of notation Index of terms.
