Adjoint functors on the derived category of motives
Abstract
Voevodsky's derived category of motives is the main arena today for the study of algebraic cycles and motivic cohomology. In this paper we study whether the inclusions of three important subcategories of motives have a left or right adjoint. These adjoint functors are useful constructions when they exist, describing the best approximation to an arbitrary motive by a motive in a given subcategory. We find a fairly complete picture: some adjoint functors exist, including a few which were previously unexplored, while others do not exist because of the failure of finite generation for Chow groups in various situations. For some base fields, we determine exactly which adjoint functors exist.
 Publication:

arXiv eprints
 Pub Date:
 February 2015
 DOI:
 10.48550/arXiv.1502.05079
 arXiv:
 arXiv:1502.05079
 Bibcode:
 2015arXiv150205079T
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Algebraic Topology;
 14F42;
 14C15;
 18E30
 EPrint:
 18 pages