Vestnik of Samara University. Natural Science SeriesVestnik of Samara University. Natural Science Series2541-75252712-8954Samara National Research University447410.18287/2541-7525-2015-21-6-98-101GERSTEN COMPLEX FOR SHEAVES WITH TRANSFERS FOR NOETHERIAN SCHEMESMingazovA.A.morenov.sv@ssau.ruSt. Petersburg Department of V.A. Steklov Institute of Mathematics of the Russian
Academy of Sciences17062015216981011705201717052017Copyright © 2015, Mingazov A.2015V. Voevodsky introduced Gersten complex for sheaves with transfers in one of the ﬁrst papers where the category of motives was constructed. Becides he proved Gersten conjecture which states that the Gersten complex for the local ring of point of smooth variety over ﬁeld k is resolution of the group of global sections over this ring. Because of this fundamental fact Gersten complex can be used for calculations of cohomologies of sheaves with transfers over smooth k -varieties. In this paper we construct Gersten complex for sheaves with trans- fers, which deﬁned on the category of noetherian k -schemes, where char k = 0. After this we proof the Gersten conjecture in case of local noetherian ring over ﬁeld k . This generalises Voevodsky’s result.пучок с трансферамигипотеза Герстенаравнохарактеристическое кольцомотивы Воеводскогогомоморфизм Гизинатрансфернетерова схемараздутиеsheaf with transfer, Gersten conjecture, equicharacteristic ring, Voevodsky motives, Gysin homomorphism, transfer, noetherian scheme, blow up