2017/04/20 by Gonçalo Tabuada, Goncalo Tabuada, Tabuada, Goncalo · 1 citation
Mathematics · #11S40 #13D15 #14A22 #14C15 #14C25 #14F30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Representation Theory (math.RT) #math.AG #math.AT #math.KT #math.RT #msc:11S40 #msc:13D15 #msc:14A22 #msc:14C15 #msc:14C25 #msc:14F30
paper · pdf · doi:10.48550/arxiv.1704.06252
11 pages
arxiv created 2017/04/20 · openalex publication_date 2017/04/20 · arxiv updated 2017/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let k be a finite base field. In this note, making use of topological periodic cyclic homology and of the theory of noncommutative motives, we prove that the numerical Grothendieck group of every smooth proper dg k-linear category is a finitely generated free abelian group. Along the way, we prove moreover that the category of noncommutative numerical motives over k is abelian semi-simple, as conjectured by Kontsevich. Furthermore, we show that the zeta functions of endomorphisms of noncommutative Chow motives are rational and satisfy a functional equation.