  This text is based on a talk by the first named author at the first congress
of the SMF (Tours, 2016). We present Bloch's conductor formula, which is a
conjectural formula describing the change of topology in a family of algebraic
varieties when the parameter specialises to a critical value. The main
objective of this paper is to describe a general approach to the resolution of
Bloch's conjecture based on techniques from both non-commutative geometry and
derived geometry.
