Higher K-theory of Koszul cubes
نویسنده
چکیده
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 f1, · · · , fp, we define Kos(A; f1, · · · , fp) the category of Koszul cubes associated to f1, · · · , fp 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; f1, · · · , fp) with that of Wt(SpecA on V (f1, · · · , fp)) defined in [HM08]. As its corollary, we get a weakly affirmative answer of the question in [DVR] and get a generalization in [PID].
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