A1homotopy theory of noncommutative motives
Abstract
In this article we continue the development of a theory of noncommutative motives. We construct categories of A1homotopy noncommutative motives, described their universal properties, and compute their spectra of morphisms in terms of KaroubiVillamayor's Ktheory (KV) and Weibel's homotopy Ktheory (KH). As an application, we obtain a complete classification of all the natural transformations defined on KV, KH. This leads to a streamlined construction of Weibel's homotopy Chern character from KV to periodic cyclic homology. Along the way we extend DwyerFriedlander's etale Ktheory to the noncommutative world, and develop the universal procedure of forcing a functor to preserve filtered homotopy colimits.
 Publication:

arXiv eprints
 Pub Date:
 February 2014
 arXiv:
 arXiv:1402.4432
 Bibcode:
 2014arXiv1402.4432T
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Algebraic Topology;
 Mathematics  KTheory and Homology;
 14A22;
 14C15;
 16E20;
 16E40;
 19D35;
 19D55;
 19L10
 EPrint:
 19 pages