17/07/2013, 16:30 — 17:30 — Sala P3.10, Pavilhão de Matemática Anthony Blanc, Université de Montpellier 2
Topological K-theory of complex non-commutative Spaces
It was known for some time by Bondal and Toën that an appropriate
notion of topological K-theory of dg-categories will furnish a
candidate for a rational structure on the periodic cyclic homology
of a smooth and proper dg-category. The main motivation comes from
the conjecture by Katzarkov-Kontsevich-Pantev that there exists a
pure non-commutative Hodge structure on the periodic homology of a
smooth and proper dg-algebra. I will present a meaningful
definition of topological K-theory of dg-categories over the
complex, using the topological Betti realization functor. This
definition is based on non-trivial results involving a
generalization of Deligne's proper cohomological descent. Finally I
will talk about the case of finite dimensional algebras.
