Non-commutative geometry, trace formula and Bloch's conductor formula

The Bloch conductor formula expresses the variations of Euler characteristics in a family of proper varieties
when the parameter specialises to a singular value. In this talk, I will present a general approach to this
conjecture based on ideas coming from non-commutative geometry. I will explain how we can use the stable
homotopy theory of schemes in order to obtain a trace formula for non-commutative spaces, and how this
trace formula can be applied to the setting of the Bloch's conductor formula.