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clifford modules

Journal of K-Theory (1)

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Clifford modules and invariants of quadratic forms
Max Karoubi, Jean-Pierre Serre
Journal:

Journal of K-Theory / Volume 9 / Issue 1 / February 2012

Published online by Cambridge University Press:

22 March 2011, pp. 1-44

Print publication:

February 2012
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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.