7/25/2023 0 Comments Spectral sequences![]() Gabber, O., K-theory of henselian local rings and henselian pairs, preprint (1985). Friedlander, Etale K-theory and arithmetic, Trans. Editorial Sudamericana Sociedad Anónima (1963), translated as Hopscotch, Random House (1966).ĭwyer, W., and E. 8 (1980), 603–622.Ĭollino, A., Quittais K-theory and algebraic cycles on almost non-singular varieties. W., Localization in lower algebraic K-theory, Comm. ![]() Kan, Homotopy Limits, Completions and Localizations, Springer Lect. Gersten, Algebraic K-theory as generalized sheaf cohomology, Higher K-Theories, Springer Lect. Bielefeld (1978).īrown, K., Abstract homotopy theory and generalized sheaf cohomollogy, Trans. F., Stable Homotopy and Generalized Homotopy, University of Chicago Press, (1974).īass, H., Algebraic K-Theory, Benjamin (1968).īrinkmann, K.-H., Diplomarbeit, Univ. This process is experimental and the keywords may be updated as the learning algorithm improves.Īdams, J. ![]() These keywords were added by machine and not by the authors. Indeed most known results in K-theory can be improved by the methods of this paper, by removing now unnecessary regularity, affineness, and other hypotheses. These new results include the “Bass fundamental theorem” 6.6, the Zariski (Nisnevich) cohomolog-ical descent spectral sequence that reduces problems to the case of local (hensel local) rings 10.3 and 19.8, the Mayer-Vietoris theorem for open covers 8.1, invariance mod ℓ under polynomial extensions 9.5, Vorst-van der Kallen theory for NK 9.12, Goodwillie and Ogle-Weibel theorems relating K-theory to cyclic cohomology 9.10, mod ℓ Mayer-Vietoris for closed covers 9.8, and mod ℓ comparison between algebraic and topological K-theory 11.5 and 11.9. Hence our theorem unleashes a pack of new basic results hitherto known only under very restrictive hypotheses like regularity. ![]() The previous lack of an adequate localization theorem for K-theory has obstructed development of this theory for the fifteen years since 1973. The localization theorem of Quillen for K′- or G-theory is the main support of his many results on the G-theory of noetherian schemes. In this paper we prove a localization theorem for the K-theory of commutative rings and of schemes, Theorem 7.4, relating the K-groups of a scheme, of an open subscheme, and of the category of those perfect complexes on the scheme which are acyclic on the open subscheme. ![]()
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