Joint IAS/PU Arithmetic Geometry

Let $X/S$ be a regular scheme over the spectrum of a discrete valuation ring. Bloch conjectured a formula relating algebraic differential forms to the total dimension of the vanishing cohomology of $X/S$. In this talk, I will explain a proof of this conjecture using tools from derived and non-commutative algebraic geometry. This is joint work with Massimo Pippi.