  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 local Hilbert functor to local
cohomology. With suitable assumptions, we use this map to answer a question of
Bloch on constructing a natural transformation from local Hilbert functor to
cohomological Chow groups.
