@book {serre, AUTHOR = {Serre, J.-P.}, TITLE = {Alg\`ebre locale. {M}ultiplicit\'es}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {1965}, PAGES = {vii+188 pp. (not consecutively paged)}, MRCLASS = {13.95 (14.08)}, MRNUMBER = {34 #1352}, MRREVR = {M. Nagata}, } @incollection {mennicke, AUTHOR = {Suslin, A.}, TITLE = {Mennicke symbols and their applications in the ${K}$-theory of fields}, PAGES = {334--356}, CROSSREF = {lnm966}, } @article {manin, AUTHOR = {Manin, Ju.}, TITLE = {Correspondences, motifs and monoidal transformations}, JOURNAL = {Mat. Sb. (N.S.)}, VOLUME = {77 (119)}, YEAR = {1968}, PAGES = {475--507}, MRCLASS = {14.47}, MRNUMBER = {41 #3482}, MRREVR = {J. W. S. Cassels}, } @article {homgenlin, AUTHOR = {Nesterenko, Yu. and Suslin, A.}, TITLE = {Homology of the general linear group over a local ring, and {M}ilnor's ${K}$-theory}, JOURNAL = {Izv. Akad. Nauk SSSR Ser. Mat.}, FJOURNAL = {Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya}, VOLUME = {53}, YEAR = {1989}, NUMBER = {1}, PAGES = {121--146}, ISSN = {0373-2436}, MRCLASS = {20G35 (14C35 19D45 19D55 19E15)}, MRNUMBER = {90a:20092}, MRREVR = {L. N. Vaserstein}, } @article {svin, AUTHOR = {Suslin, A. and Voevodsky, V.}, TITLE = {Singular homology of abstract algebraic varieties}, JOURNAL = {Invent. Math.}, FJOURNAL = {Inventiones Mathematicae}, VOLUME = {123}, YEAR = {1996}, NUMBER = {1}, PAGES = {61--94}, ISSN = {0020-9910}, CODEN = {INVMBH}, MRCLASS = {14F99 (14C25 14F20 19E15)}, MRNUMBER = {97e:14030}, MRREVR = {Eric M. Friedlander}, } @inproceedings {milnring, AUTHOR = {Bass, H. and Tate, J.}, TITLE = {The {M}ilnor ring of a global field}, BOOKTITLE = {Algebraic $K$-theory, II: ``Classical'' algebraic $K$-theory and connections with arithmetic (Proc. Conf., Seattle, Wash., Battelle Memorial Inst., 1972)}, PAGES = {349--446. 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M. and Voevodsky, V.}, TITLE = {{Bivariant Cycle Cohomology}}, PAGES = {138--187}, CROSSREF = {orange}, } @inproceedings {bk, EDITOR = {{B. Gordon, J. Lewis, S. M\"{u}ller-Stach, S. Saito, N. Yui}}, AUTHOR = {Suslin, A. and Voevodsky, V.}, BOOKTITLE = {The Arithmetic and Geometry of Algebraic Cycles}, TITLE = {{B}loch-{K}ato Conjecture and Motivic Cohomology with finite coefficients}, PAGES = {117--189}, VOLUME = {548}, YEAR = {2000}, PUBLISHER = {Kluwer}, SERIES = {Nato ASI series C}, } @book {ega1sv, AUTHOR = {Grothendieck, A. and Dieudonn\'{e}, J.}, TITLE = {\'{E}l\'ements de g\'eom\'etrie alg\'ebrique 1}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1971}, KEY = {ega0}, } @article {hmov, AUTHOR = {Bloch, S.}, TITLE = {The moving lemma for higher {C}how groups}, JOURNAL = {J. Algebraic Geom.}, FJOURNAL = {Journal of Algebraic Geometry}, VOLUME = {3}, YEAR = {1994}, NUMBER = {3}, PAGES = {537--568}, ISSN = {1056-3911}, MRCLASS = {14C15 (14C25 14C35)}, MRNUMBER = {96c:14007}, MRREVR = {Claudio Pedrini}, } @article {acahkt, AUTHOR = {Bloch, S.}, TITLE = {Algebraic cycles and higher ${K}$-theory}, JOURNAL = {Adv. in Math.}, FJOURNAL = {Advances in Mathematics}, VOLUME = {61}, YEAR = {1986}, NUMBER = {3}, PAGES = {267--304}, ISSN = {0001-8708}, CODEN = {ADMTA4}, MRCLASS = {18F25 (11G45 14C35 19D99 19E15)}, MRNUMBER = {88f:18010}, MRREVR = {L. N. Vaserstein}, } @incollection {bg, AUTHOR = {Brown, K. S. and Gersten, S. M.}, TITLE = {Algebraic ${K}$-theory as generalized sheaf cohomology}, BOOKTITLE = {Algebraic K-theory, I: Higher K-theories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972)}, PAGES = {266--292. 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Verdier}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {1972-1973}, KEY = {SGA}, } @article {rickard, AUTHOR = {Rickard, J.}, TITLE = {Derived categories and stable equivalence}, JOURNAL = {J. Pure Appl. Algebra}, FJOURNAL = {Journal of Pure and Applied Algebra}, VOLUME = {61}, YEAR = {1989}, NUMBER = {3}, PAGES = {303--317}, ISSN = {0022-4049}, CODEN = {JPAAA2}, MRCLASS = {16D90 (16G30 16S90 18E30 20C05)}, MRNUMBER = {91a:16004}, MRREVR = {Dieter Happel}, } @book {hart, AUTHOR = {Hartshorne, R.}, TITLE = {Algebraic geometry}, NOTE = {Graduate Texts in Mathematics, No. 52}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1977}, PAGES = {xvi+496}, ISBN = {0-387-90244-9}, MRCLASS = {14-01}, MRNUMBER = {57 #3116}, MRREVR = {Robert Speiser}, } @article {mv, AUTHOR = {Morel, F. and Voevodsky, V.}, TITLE = {${\bf {A}}\sp 1$-homotopy theory of schemes}, JOURNAL = {Inst. Hautes \'Etudes Sci. Publ. Math.}, FJOURNAL = {Institut des Hautes \'Etudes Scientifiques. Publications Math\'ematiques}, NUMBER = {90}, YEAR = {1999}, PAGES = {45--143 (2001)}, ISSN = {0073-8301}, CODEN = {PMIHA6}, MRCLASS = {14Fxx}, MRNUMBER = {1 813 224}, } @article {ega1, AUTHOR = {Grothendieck, A.}, TITLE = {\'{E}l\'ements de g\'eom\'etrie alg\'ebrique. {I}. {L}e langage des sch\'emas}, JOURNAL = {Inst. Hautes \'Etudes Sci. Publ. Math.}, NUMBER = {4}, YEAR = {1960}, PAGES = {228}, MRCLASS = {14.55}, MRNUMBER = {36 \#177a}, KEY = {ega1}, NOTE = {Reprinted in \cite{ega1sv}}, } @article {ega2, AUTHOR = {Grothendieck, A.}, TITLE = {\'{E}l\'ements de g\'eom\'etrie alg\'ebrique. {I}{I}. \'{E}tude globale \'el\'ementaire de quelques classes de morphismes.}, JOURNAL = {Inst. Hautes \'Etudes Sci. Publ. 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Publ. Math.}, NUMBER = {20}, YEAR = {1964}, MRCLASS = {14.05 (13.10)}, MRNUMBER = {30 \#3885}, MRREVIEWER = {H. Hironaka}, KEY = {ega0}, NOTE = {Reprinted in \cite{ega1sv}}, } @article {tohoku, AUTHOR = {Grothendieck, A.}, TITLE = {Sur quelques points d'alg\`ebre homologique}, JOURNAL = {T\^ohoku Math. J. (2)}, VOLUME = {9}, YEAR = {1957}, PAGES = {119--221}, MRCLASS = {18.00}, MRNUMBER = {21 \#1328}, MRREVIEWER = {D. Buchsbaum}, } @incollection {verdier, AUTHOR = {Verdier, J.-L.}, TITLE = {Cat\'egories d\'eriv\'ees, \'etat 0}, CROSSREF = {sga4.5}, } @article {maninha, AUTHOR = {Manin, Ju.}, TITLE = {Lectures on the ${K}$-functor in algebraic geometry}, JOURNAL = {Uspehi Mat. Nauk}, VOLUME = {24}, YEAR = {1969}, NUMBER = {5 (149)}, PAGES = {3--86}, MRCLASS = {14.00}, MRNUMBER = {42 \#265}, MRREVIEWER = {M. L. 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Algebra}, VOLUME = {21}, YEAR = {1972}, PAGES = {113--136}, MRCLASS = {18F25}, MRNUMBER = {47 \#1916}, MRREVIEWER = {H. Bass}, } @book {sga4.5, AUTHOR = {Deligne, P.}, TITLE = {Cohomologie \'etale}, NOTE = {S\'eminaire de G\'eom\'etrie Alg\'ebrique du Bois-Marie SGA 4${\frac12}$, Avec la collaboration de J.-F. Boutot, A. Grothendieck, L. Illusie et J.-L. Verdier, Lecture Notes in Mathematics, Vol. 569}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {1977}, PAGES = {iv+312pp}, MRCLASS = {14F20}, MRNUMBER = {57 \#3132}, MRREVIEWER = {J. S. Milne}, } @book {lnm966, TITLE = {Algebraic ${K}$-theory. {P}art {I}{I}}, BOOKTITLE = {Proceedings of a Conference held at Oberwolfach, June 16--20, 1980}, EDITOR = {Dennis, R.~K.}, PUBLISHER = {Springer-Verlag}, ADDRESS = {Berlin}, YEAR = {1982}, PAGES = {viii+409}, ISBN = {3-540-11966-3}, MRCLASS = {18-06 (16-06 16A54 18F25)}, MRNUMBER = {84a:18001b}, } %___________________________________________ % added by CAW for INTRO %_______________________________ @article {BMS, AUTHOR = {A. Beilinson, R. MacPherson and V. Schechtman}, TITLE = {Notes on motivic cohomology}, JOURNAL = {Duke Math. J.}, VOLUME = {54}, YEAR = {1987}, PAGES = {679--710}, MRNUMBER = {88f:14021}, KEY = {BMS87}, } @inproceedings {Levine2, AUTHOR = {Levine, M.}, TITLE = {Bloch's higher Chow groups revisited}, BOOKTITLE = {$K$-theory (Strasbourg, 1992)}, YEAR = {1994}, PAGES = {235--320}, MRNUMBER = {96c:14008}, } @incollection {Licht2, AUTHOR = {Lichtenbaum, S.}, TITLE = {Values of zeta-functions at nonnegative integers}, BOOKTITLE = {Number theory, Noordwijkerhout 1983 (Noordwijkerhout, 1983)}, PAGES = {127--138}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1984}, MRCLASS = {11G40 (14G10)}, MRNUMBER = {756 089}, } @unpublished {MC, AUTHOR = {Voevodsky, V.}, TITLE = {The {M}ilnor {C}onjecture}, NOTE = {Preprint. http://www.math.uiuc.edu/K-theory/170}, YEAR = {1996}, } @unpublished {Cancellation, AUTHOR = {Voevodsky, V.}, TITLE = {{C}ancellation theorem}, NOTE = {Preprint. http://www.math.uiuc.edu/K-theory/541}, YEAR = {2002}, } @unpublished {BL, AUTHOR = {S.~Bloch and S.~Lichtenbaum}, TITLE = {A spectral sequence for motivic cohomology}, NOTE = {Preprint, to appear in Inventiones Math.}, YEAR = {1994}, } @unpublished {FS, AUTHOR = {E. M. Friedlander and A. Suslin}, TITLE = {The spectral sequence relating algebraic $K$-theory to motivic cohomology}, NOTE = {Preprint. http://www.math.uiuc.edu/K-theory/0432}, YEAR = {2000}, } @book {mm, AUTHOR = {Levine, M.}, TITLE = {Mixed motives}, PUBLISHER = {American Mathematical Society}, ADDRESS = {Providence, RI}, YEAR = {1998}, PAGES = {x+515}, ISBN = {0-8218-0785-4}, MRCLASS = {14F99 (14C15 14C25 14C35 18E30 19E08)}, MRNUMBER = {99i:14025}, MRREVIEWER = {Luca Barbieri Viale}, } @incollection {nistop, AUTHOR = {Nisnevich, Ye. A.}, TITLE = {The completely decomposed topology on schemes and associated descent spectral sequences in algebraic ${K}$-theory}, BOOKTITLE = {Algebraic $K$-theory: connections with geometry and topology (Lake Louise, AB, 1987)}, PAGES = {241--342}, PUBLISHER = {Kluwer Acad. Publ.}, ADDRESS = {Dordrecht}, YEAR = {1989}, MRCLASS = {19E20 (14C35 19F05 20G10)}, MRNUMBER = {91c:19004}, MRREVIEWER = {J. F. Jardine}, } @book {adams, AUTHOR = {Adams, J. F.}, TITLE = {Stable homotopy and generalised homology}, NOTE = {Chicago Lectures in Mathematics}, PUBLISHER = {University of Chicago Press}, ADDRESS = {Chicago, Ill.}, YEAR = {1974}, PAGES = {x+373}, MRCLASS = {}, MRNUMBER = {53 \#6534}, MRREVIEWER = {P. S. Landweber}, } @book {whitehead, AUTHOR = {Whitehead, George W.}, TITLE = {Elements of homotopy theory}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1978}, PAGES = {xxi+744}, ISBN = {0-387-90336-4}, MRCLASS = {}, MRNUMBER = {80b:55001}, MRREVIEWER = {Brayton Gray}, } @incollection {ks, AUTHOR = {Kato, K. and Saito, S.}, TITLE = {Global class field theory of arithmetic schemes}, BOOKTITLE = {Applications of algebraic $K$-theory to algebraic geometry and number theory, Part I, II (Boulder, Colo., 1983)}, PAGES = {255--331}, PUBLISHER = {Amer. Math. 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Conf., Battelle Memorial Inst., Seattle, Wash., 1972)}, PAGES = {293--316. Lecture Notes in Math., Vol. 341}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1973}, MRCLASS = {14F15}, MRNUMBER = {53 \#13231}, MRREVIEWER = {Manuel Ojanguren}, } @article {swanvbpm, AUTHOR = {Swan, R.~G.}, TITLE = {Vector bundles and projective modules}, JOURNAL = {Trans. Amer. Math. Soc.}, VOLUME = {105}, YEAR = {1962}, PAGES = {264--277}, MRCLASS = {57.30 (13.40)}, MRNUMBER = {26 \#785}, MRREVIEWER = {K. Kondo}, }