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Bloch's formula

Result in algebraic K-theory relating Chow groups to cohomology From Wikipedia, the free encyclopedia

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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; is the sheaf associated to the presheaf , U Zariski open subsets of X. The general case is due to Quillen.[1] For q = 1, one recovers . (see also Picard group.)

The formula for the mixed characteristic is still open.

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