Products of degenerate quadratic forms

2005/11/01 by Paul Balmer · 13 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Degenerate energy levels #Duality (order theory) #Geometry #Homotopy and Cohomology in Algebraic Topology #Mathematics #Nonlinear Waves and Solitons #Product (mathematics) #Pure mathematics #Quadratic equation #Tensor product #Type (biology)

paper · pdf · doi:10.1112/s0010437x05001508

published in Compositio Mathematica 141(6), 1374-1404 (Cambridge University Press)

openalex publication_date 2005/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

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.

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