Noncommutative Geometry in the Framework of Differential Graded Categories
arXiv:0805.1628 · doi:10.1007/978-0-8176-4831-2_9
Abstract
In this survey article we discuss a framework of noncommutative geometry with differential graded categories as models for spaces. We outline a construction of the category of noncommutative spaces and also include a discussion on noncommutative motives. We propose a motivic measure with values in a motivic ring. This enables us to introduce certain zeta functions of noncommutative spaces.
19 pages. Minor corrections and one reference added; to appear in the proceedings volume of AGAQ Istanbul, 2006