There is an introduction in Gillet: K-theory and Intersection theory. It is something that you prove for a cohomology theory.
http://mathoverflow.net/questions/82786/state-of-the-art-for-gerstens-conjecture-for-k-theory
Gabber: Gersten’s conjecture for some complexes of vanishing cycles (1994)
Snaith: Stable homotopy around the Arf-Kervaire invariant (PIM 273), in Homotopy folder. For the Gersten conjecture, see the book references numbered 67, 82, 83, 88, 89, 139, 199, 213, 232, 241, 271.
A proof by Mochizuki, apparently a correction is found here. “The purpose of this article is to prove that Gersten’s conjecture for K_0-groups of a commutative regular local ring is true. As its applications, we will obtain the vanishing conjecture for certain Chow groups, generator conjecture for certain K-groups.” See also http://www.math.uiuc.edu/K-theory/0842. Apparently, there are some mistakes still.
http://www.math.uiuc.edu/K-theory/0568: We prove the Gersten conjecture for Witt groups in the equicharacteristic case.
Barbieri-Viale: K-cohomology and local algebraic cycles (1990). Could possibly be interesting, but is in Italian.
Gersten conjecture for etale cohomology, see Colliot-Thelene: Birational invariants, Purity, and the Gersten conjecture. In Proc. Symp. Pure Math. vol 58.1 (1995).
Gabber has an article, approx 1994, on the Gersten conjecture for some complexes of vanishing cycles. Looks good, in Manuscripta.
Title: Gersten Conjecture For Equivariant K-theory And Applications. Authors: Amalendu Krishna. For a reductive group scheme over a regular semi-local ring, we prove an equivarinat version of the Gersten conjecture. We draw some interesting consequences for the representation rings of such reductive group schemes. We also prove the rigidity for the equivariant K-theory of reductive group schemes over a henselian local ring. This is then used to compute the equivariant K-theory of algebraically closed fields. http://arxiv.org/abs/0906.3933
nLab page on Gersten conjecture