K-theory of rational quadratic forms

2017/11/02 by Igor Nikolaev, Nikolaev, Igor
Mathematics · #11E16 #46L85 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1711.00743

openalex publication_date 2017/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the genus of a rational quadratic form in terms of the K-theory of a C*-algebra attached to the adelic orthogonal group of the form. As a corollary, one gets a higher composition law for the rational quadratic forms. As an illustration, we consider the Gauss composition of the binary quadratic forms.

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