Second differentials in the Quillen spectral sequence

Abstract

For an algebraic variety $X$ we introduce generalized first Chern classes, which are defined for coherent sheaves on $X$ with support in codimension $p$ and take values in $C{H}^p(X)$. We use them to provide an explicit formula for the differentials $d_2^p:E_2^{p,-p-1}\to E_2^{p+2,-p-2}\cong C{H}^{p+2}(X)$ in the Quillen spectral sequence.

8 pages; v.2: simplified proof of the main result, minor corrections in other sections