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Clifford modules and invariants of quadratic forms

Published online by Cambridge University Press:  22 March 2011

Max Karoubi  and
Jean-Pierre Serre
Max Karoubi
Affiliation:
Université Denis Diderot- Paris 7, UFR de Mathématiques, Case 7012, 175, rue du Chevaleret, 75205 Paris cedex 13, France, max.karoubi@gmail.com
Jean-Pierre Serre
Affiliation:
Collège de France, Place Marcelin Berthelot, 75005 Paris, France, serre@noos.fr
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Abstract

We construct new invariants of quadratic forms over commutative rings, using ideas from Topology. More precisely, we define a hermitian analog of the Bott class with target algebraic K-theory, based on the classification of Clifford modules. These invariants of quadratic forms go beyond the classical invariants defined via the Clifford algebra. An appendix by J.-P. Serre, of independent interest, describes the “square root” of the Bott class in the general framework of lambda rings.

Keywords

Quadratic formsClifford modulesBott classalgebraic K-theorylambda rings
Type
Research Article
Information
Journal of K-Theory , Volume 9 , Issue 1 , February 2012 , pp. 1 - 44
Copyright
Copyright © ISOPP 2011

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