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

TL;DR

This paper explores the extension of Bloch's formula using Bloch-Ogus theorem and cyclic homology, constructing maps between local Hilbert functors and cohomological Chow groups to advance understanding of algebraic cycles.

Contribution

It provides new insights into extending Bloch's formula and constructs natural transformations linking local Hilbert functors to cohomological Chow groups.

Findings

Extended Bloch formula via Bloch-Ogus theorem and cyclic homology.

Constructed a map from local Hilbert functor to local cohomology.

Answered questions of Green, Griffiths, and Bloch on algebraic cycles.

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 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.