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cmr10NIKIT*AUUA.KARPENKOANDALEXANDERS.MERKURJEV `$ -
cmcsc10Abstract.\`Let
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cmmi10pӲbGeaprimeintegerandFcaeldofcharacteristic0..LetXUbGethe ':
cmti10norm $ variety8ofa8symbGolintheGaloiscohomologygroupH ^ 0er cmmi7nٓR cmr7+1a(FG;^O! cmsy7
np)(forsomenA
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cmsy10A1),$ constructed>intheproGof>oftheBloch-Katoconjecture..Themain>resultofthepaper$ arms
]that
\thefunctioneldFc(X )hasthefollowingpropGerty:LKfor
\anyequidimensional$ vqarietyY8,thechangeofeldhomomorphismCHkp(Y8)!CH(Y:F(X J) )ofChowgroupswith:$ coGecientsinintegersloGcalizedatpissurjectiveincoGdimensions<(dimUVX )=(p 1).1One$ ofOthemainOingredientsoftheproGofisacomputationofChowgroupsofa(generalized)$ Rostmotive(avqariantofthemainresultnotrelyingonthisisgiveninAppGendix).$ AnotherֶimpGortantingredientַisA-trivialityofX ,thepropGertysayingַthatthedegree$ homomorphismK,onK+CH0(XLt)isK+injectiveforanyK+eldextensionL=FwithX (L)`Ѹ6=;.$ TheAproGofBinvolvestheBtheoryofrationalcorrespGondences,duetoMarkusRost,reviewed$ inUUAppGendix. Ƌ"-
cmcsc10Contents html: html: html:XQ cmr121.InrtroSduction html:`/2 html:2.%g cmmi12A-trivialvXarieties html:F3 html:3.AbstractRostmotivres html:,5 html:4.GenericsplittingvXarieties html:j9 html:5.A-trivialitryofstandardnormvXarieties html: