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1、MathematicalSurveysandMonographsVolume57MixedMotivesMarcLevineATHEMATICMALNTRHTOSMHEISITWSAOICCIREAmericanMathematicalSocietyEAGEWMETMYAF8O8UNDED18EditorialBoardGeorgiaBenkartTudorStefanRatiu,ChairHowardA.MasurMichaelRenardy1991MathematicsSubjectClassification.Primary19E15,1
2、4C25;Secondary14C15,14C17,14C40,19D45,19E08,19E20.ResearchsupportedinpartbytheNationalScienceFoundationandtheDeutscheForschungsgemeinschaft.Abstract.Theauthorconstructsanddescribesatriangulatedcategoryofmixedmotivesoveranarbitrarybasescheme.Theresultingcohomologytheorysatis
3、fiestheBloch-Ogusaxioms;ifthebaseschemeisasmoothschemeofdimensionatmostoneoverafield,thiscohomologytheoryagreeswithBloch’shigherChowgroups.Mostoftheclassicalconstructionsofcohomologycanbemadeinthemotivicsetting,includingChernclassesfromhigherK-theory,push-forwardforpropermaps
4、,Riemann-Roch,duality,aswellasanassociatedmotivichomology,Borel-Moorehomologyandcohomologywithcompactsupports.ThemotiviccategoryadmitsarealizationfunctorforeachBloch-Oguscohomologytheorywhichsatisfiescertainaxioms;asexamplestheauthorconstructsBetti,etale,andHodgerealizations
5、oversmoothbaseschemes.Thisbookisacombinationoffoundationalconstructionsinthetheoryofmotives,togetherwithresultsrelatingmotiviccohomologywithmoreexplicitconstructions,suchasBloch’shigherChowgroups.Itisaimedatresearchmathematiciansinterestedinalgebraiccycles,motivesandK-theor
6、y,startingatthegraduatelevel.Itpresupposesabasicbackgroundinalgebraicgeometryandcommutativealgebra.LibraryofCongressCataloging-in-PublicationDataLevine,Marc,1952–Mixedmotives/MarcLevine.p.cm.—(Mathematicalsurveysandmonographs,ISSN0076-5376;v.57)Includesbibliographicalrefere
7、ncesandindexes.ISBN0-8218-0785-4(acid-free)1.Motives(Mathematics)I.Title.II.Series:Mathematicalsurveysandmonographs;no.57.QA564.L481998516.35—dc2198-4734CIPCopyingandreprinting.Individualreadersofthispublication,andnonprofitlibrariesactingforthem,arepermittedtomakefairuseof
8、thematerial,suchastocopyachapterforuseinteachingorresearch.Permissionisgrantedtoqu
