The main objective of this paper is generalizing a notion of Koszul resolutions and characterizing modules which admits such a resolution. We turn out that for a noetherian domain A and a coherent A module M, M has a two dimensional generalized Koszul resolution if and only if M is a pure weight two modules in the sense of [HM09]. As its applications, we are attacking the Gersten conjecture for weight two case.
Satoshi Mochizuki <email@example.com>
Akiyoshi Sannai <firstname.lastname@example.org>