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Noncommutative Geometry in the Framework of Differential Graded Categories

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Book cover Arithmetic and Geometry Around Quantization

Part of the book series: Progress in Mathematics ((PM,volume 279))

Summary

In this survey 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.

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Authors and Affiliations

  1. Dept. of Math., University of Toronto, Toronto, Canada

    Snigdhayan Mahanta

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  1. Snigdhayan Mahanta
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Correspondence to Snigdhayan Mahanta .

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Editors and Affiliations

  1. MPI für Mathematik, Vivatsgasse 7, Bonn, 53111, Germany

    Özgür Ceyhan  & Yu. I. Manin  & 

  2. Department of Mathematics, California Institute of Technology, 1200 E . California Blvd., Pasadena, CA, 91125, USA

    Matilde Marcolli

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Mahanta, S. (2010). Noncommutative Geometry in the Framework of Differential Graded Categories. In: Ceyhan, Ö., Manin, Y.I., Marcolli, M. (eds) Arithmetic and Geometry Around Quantization. Progress in Mathematics, vol 279. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4831-2_9

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