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
References in corpus (18)
- The elliptic curve in the S-duality theory and Eisenstein series for Kac-Moody groups
- Categories of holomorphic vector bundles on noncommutative two-tori
- Lectures on Noncommutative Geometry
- Perverse coherent sheaves (after Deligne)
- Duality and equivalence of module categories in noncommutative geometry I
- Derived Algebraic Geometry III: Commutative Algebra
- The Grothendieck ring of varieties is not a domain
- Presheaves of triangulated categories and reconstruction of schemes
- Number theory and dynamical systems on foliated spaces
- Theorie homotopique des DG-categories
- Grothendieck ring of pretriangulated categories
- Duality and equivalence of module categories in noncommutative geometry II: Mukai duality for holomorphic noncommutative tori
- Motivic integration and the Grothendieck group of pseudo-finite fields
- A-infinity algebras, modules and functor categories
- Bost-Connes-Marcolli systems for Shimura varieties. I. Definitions and formal analytic properties
- Derived Algebraic Geometry II: Noncommutative Algebra
- On the structure of Calabi-Yau categories with a cluster tilting subcategory
- A-infinity-bimodules and Serre A-infinity-functors