The Gersten resolution or Gersten complex is certain exact sequence of abelian sheaves on a Zariski site, used for the computation of higher algebraic K-theory groups. One way of deriving it is from a spectral sequence related to the study of motivic sheaves.
The exactness of the Gersten complex for affine regular, equicharacteristic excellent local rings with infinite residue field (or the like) is also known as the Gersten conjecture (see e.g. Kerz 08, p. 4).
Original references include
Daniel Quillen, Algebraic K-theory, I: Higher K-theories (Battelle Memorial Inst., Seattle 1972), Proc. Conf., Lecture Notes in Math. 341, 1973, pp. 85–147.
Spencer Bloch, Algebraic cycles and higher K-theory, Adv. in Math. 61 (1986), 267–304.
Review includes
Ishai Dan-Cohen, Bloch’s formula and the Gersten resolution (pdf)
Moritz Kerz, Milnor K-theory of local rings Dissertation, Universität Regensburg (2008) (web)
Thomas Geisser, Motivic cohomology, K-theory and topological cyclic homology, chapter II.1 in Handbook of K-theory, pdf
See also