Seminário de Álgebra  RSS

17/07/2013, 16:30 — 17:30 — Sala P3.10, Pavilhão de Matemática
, 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.

Organizador actual: Gustavo Granja

CAMGSD FCT