I am trying to emerge from my complete ignorance about intersection theory. I have a bias toward sheaves, so I like the idea of doing intersection theory with the K-group of coherent sheaves. From what I understand the graded (by codimension) K-group GK is isomorphic to the Chow group A after tensoring with the rational numbers (and I probably need to say smooth variety).
I know of two/three places where to learn this stuff: Fulton, Lang RR algebra; the book chapter by Henri Gillet titled k-theory and intersection theroy; the set of lecture notes by Pedro Sancho de Salas http://matematicas.unex.es/~sancho/ (the link is for his webpage, which contains a few goodies).
However, the numerical group (the quotient of A modulo numerical equivalence) doesn't seem to be mentioned. The codimension one group is usually called the Neron-Severi group and is mentioned in some books, the whole group is briefly (if i recall correctly) mentioned in Fulton's book on intersection theory.
Are there any good references for the numerical group treated from the point of view of the K-group?
Is it true that GN (the graded K-group of coherent sheaves modulo numerical equivalence) is isomorphic to N, the Chow group modulo numerical equivalence) without having to tensor by the rationals?
p.s. I say two elements of K are numerically equivalent if they $\chi(-,F)$ gives the same answer for any sheaf F.