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html: html:* >RN cmbx12UPPERٚMOTIVESOFALGEBRAICGR OUPSAND +INCOMPRESSIBILITYٚOFSEVERI-BRA UERV ARIETIES pK`y
cmr10NIKIT*AUUA.KARPENKO `$ -
cmcsc10Abstract.\`Let
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cmmi10pbGeapGositiveprimeinteger.>LetGbGeasemisimpleanealgebraic $ groupxofxinnertypGeoveraxeldFc.(=W*ewrite%n
eufm10X 0er cmmi7G 2fortheclassofallnitedirectproGductsof$ pro 8jectivepG-homogeneousqFc-vqarieties.UW*edeterminethestructureofthe ':
cmti10ChowFmotives$ with#c}'oecientsin$aniteeldͭofͬthevqarietiesinXGڲ.Moreprecisely*,+itisknown$ thatmthelmotiveofanylvqarietyinlXGGdecompGoses(inauniqueway)intomasumof$ indecompGosablemotives,andwedescribGetheindecomposablesummandswhichappear$ inUUthedecompGositions.0 InQtheRcasewhereGisthegroupPGL.AofautomorphismsofagivencentralRsimpleFc-$ algebra8ʵA,>for8anyvqarietyin8theclassXG (whichincludes8thegener}'alizedySeveri-Brauer$ varieties^ofthe^algebraA)wedetermineitsc}'anonicaldimensionatanyprimep.In$ particular,wecndcoutwhichvqarietiescinXGarep-inc}'ompressible.IfAcisadivision$ algebra#of$degreep^nforsomen
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cmsy100,then#thelistofp-incompressiblevqarietiesincludes$ theNIgeneralizedNHSeveri-BrauervqarietyX (p^m;A)ofNHidealsofreduceddimensionp^mfor$ m=0;1;:::;n. ёhtml: html: