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Products of degenerate quadratic forms

Published online by Cambridge University Press:  04 December 2007

Paul Balmer
Paul Balmer
Affiliation:
D-Math, ETH Zentrum, 8092 Zürich, Switzerlandbalmer@math.ethz.chhttp://www.math.ethz.ch/˜balmer
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Abstract

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We challenge the classical belief that products of degenerate quadratic forms must remain degenerate and we show that this fails in general, e.g. over tensor triangulated categories with duality. This opens new ways of constructing non-degenerate quadratic forms and hence classes in Witt groups. In addition, we encapsulate in a Leibniz-type formula the behavior of the product with respect to the symmetric cone construction. We illustrate these ideas by computing the total Witt group of regular projective spaces.

Keywords

product of symmetric formsdegeneracyconsanguinityWitt groups11E8118E3019G12
Type
Research Article
Information
Compositio Mathematica , Volume 141 , Issue 6 , November 2005 , pp. 1374 - 1404
Copyright
Foundation Compositio Mathematica 2005