nLab Gersten resolution



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

  • S. O. Gorchinskii, Adelic resolution for sheaves of K-groups, Russ. Math. Surv. 62, p. 184-186 (2007) pdf

Last revised on September 4, 2014 at 17:34:25. See the history of this page for a list of all contributions to it.