2017/03/30 by Gonçalo Tabuada, Goncalo Tabuada, Tabuada, Goncalo
Mathematics · #14A22 #14C25 #19E08 #19E15 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #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:14A22 #msc:14C25 #msc:19E08 #msc:19E15
paper · pdf · doi:10.48550/arxiv.1703.10599
16 pages; revised version
openalex publication_date 2017/03/30 · arxiv created 2017/05/07 · arxiv updated 2017/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article we prove that the numerical Grothendieck group of every smooth proper dg category is invariant under primary field extensions, and also that the mod-n algebraic K-theory of every dg category is invariant under extensions of separably closed fields. As a byproduct, we obtain an extension of Suslin's rigidity theorem, as well as of Yagunov-Ostvaer's equivariant rigidity theorem, to singular varieties. Among other applications, we show that base-change along primary field extensions yields a faithfully flat morphism between noncommutative motivic Galois groups. Finally, along the way, we introduce the category of n-adic noncommutative mixed motives.