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html: html:* {SN cmbx12INCOMPRESSIBILITYٚOF N.GENERALIZEDٚSEVERI-BRA UERV ARIETIES pK`y
cmr10NIKIT*AUUA.KARPENKO `$ -
cmcsc10Abstract.\`Let+A
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cmmi10FвbGeanarbitraryeld.cLetAbeacentralsimpleFc-algebra.cLetGbe $ thealgebraicgroupAut]AofautomorphismsofA.vLet%n
eufm10X 0er cmmi7A
DbGetheclassofnitedirect$ proGductsofpro 8jectiveG-homogeneousFc-vqarieties(theclassXA includesthe ':
cmti10gener}'alized$ Severi-Br}'auervarietiesUUofthealgebraA).0 LetpbGeapGositiveprimeinteger.F*oranyvqarietyinXA,wedetermineitsc}'anonical$ dimension-at-ɵp.gInparticular,&iwendoutwhichvqarietiesinXA
(arep-inc}'ompressible.$ IfjAisakdivisionalgebraofdegreep^n forsomen1
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cmsy1010,othenthelistofp-incompressible$ vqarieties~ZincludesthegeneralizedSeveri-Brauervariety~YX (p^m;A)ofidealsofreduced$ dimensionUUp^m
form=0;1;:::;n.0 W*e?alsodeterminethe>structureoftheChowBmotivesBwithc}'oecientsinB
msbm10Fpof?the$ vqarieties!in XA.*Moreprecisely*,Hitisknownthatthemotiveofanyvqariety!inXA
de-$ compGosesB(inaBuniqueway)BintoaBsumofindecompGosablemotives,FeandBwedescribGethe$ indecompGosablesummandswhichappearinthedecompositions.tAnapplicationofthe$ abGoveUUresultsisaproofofthehyp}'erbolicityconjectureUUonorthogonalinvolutions. ɺhtml: html: