Bertrand Toen
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Title: Topological invariants for non-commutative schemes
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Abstract: This talk is a report on a recent work of Anthony
Blanc.
I will start by recalling the setting of non-commutative
geometry in the
sense of Bondal, Kontsevich, Van den Bergh, based on
associative
dg-algebras. I will also recall the existence of moduli spaces
(or rather stacks) of sheaves on non-commutative schemes. I
will then explain how these moduli spaces can be used in order
to define topological K-theory of non-commutative schemes, as
well as to prove that the algebraic chern character with values
in periodic cyclic homology factors throught topological
K-theory. I will finish the
talk with some open questions, relevant to non-commutative
Hodge theory in the
sense of Katzarkov-Kontsevich-Pantev, Kaledin.