Bloch-Ogus theorem, cyclic homology and deformations of Chow groups

Abstract

Using Bloch-Ogus theorem and Chern character from K-theory to cyclic homology, we answer a question of Green and Griffiths on extending Bloch formula. Moreover, we construct a map from the local Hilbert functor to local cohomology groups. With suitable assumptions, we use this map to answer a question of Bloch on constructing a natural transformation from the local Hilbert functor to cohomological Chow groups.