In algebraic K-theory, a branch of mathematics, Bloch's formula, introduced by Spencer Bloch for
, states that the Chow group of a smooth variety X over a field is isomorphic to the cohomology of X with coefficients in the K-theory of the structure sheaf
; that is, where the right-hand side is the sheaf cohomology;
, U Zariski open subsets of X.
The general case is due to Quillen.
The formula for the mixed characteristic is still open.