Motivic structures in non-commutative geometry

Details Motivic structures in non-commutative geometry Motivic structures in non-commutative geometry

2010-03-16

arxiv.org/abs/1003.3210v1

Mathematics

Algebraic Geometry

LaTeX 2e, 24 pages.

Scientific paper

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.

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