2022/06/09 by Gonçalo Tabuada, Tabuada, Goncalo
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Finite Group Theory Research #K-Theory and Homology (math.KT) #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2206.04653
openalex publication_date 2022/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, by combining the recent theory of noncommutative motives with the classical theory of motives, we prove that if two quadrics (or, more generally, two involution varieties) have the same Grothendieck class, then they have the same even Clifford algebra and the same signature. As an application, we show in numerous cases (e.g., when the base field is a local or global field) that two quadrics (or, more generally, two involution varieties) have the same Grothendieck class if and only if they are isomorphic.