Motivic structures in non-commutative geometry
Abstract
We review some recent results and conjectures saying that, roughly speaking, periodic cyclic homology of a smooth non-commutative algebraic variety should carry all the additional "motivic" structures possessed by the usual de Rham cohomology of a smooth algebraic variety (specifically, an R-Hodge structure for varieties over R, and a filtered Dieudonne module structure for varieties over Z_p). To appear in Proc. ICM 2010.
- Publication:
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arXiv e-prints
- Pub Date:
- March 2010
- DOI:
- 10.48550/arXiv.1003.3210
- arXiv:
- arXiv:1003.3210
- Bibcode:
- 2010arXiv1003.3210K
- Keywords:
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- Mathematics - Algebraic Geometry
- E-Print:
- LaTeX 2e, 24 pages.