Higher K-theory of Koszul cubes, by Satoshi Mochizuki
In this paper, for noetherian commutative ring with a unit A such that every
finitely generated A-module is free, and for a certain A-regular sequence
f_1,...,f_p, we define Kos(A; f_1,...,f_p) the category of Koszul cubes
associated to f_1,...,f_p which has a natural Waldhausen categorical
structure. We also give a new algorithm of resolution process of modules by
Koszul cubes. By the virtue of the algorithm, we get the comparison theorem
between the K-theory of Kos(A; f_1,...,f_p) with that of Wt(SpecA on V
(f_1,...,f_p) defined in [HM08]. As its corollary, we get a weakly affirmative
answer of the question in [DVR] and get a generalization in [PID].
Satoshi Mochizuki <mochi81@hotmail.com>