Noncommutative Geometry in the Framework of Differential Graded Categories

Understand

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.