Mathematics

Gersten complex for sheaves with transfers for noetherian schemes

A. A. Mingazov

St. Petersburg Department of V.A. Steklov Institute of Mathematics of the Russian Academy of Sciences, 27, Fontanka, St. Petersburg, 191023, Russian Federation

Abstract: V. 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 transfers, 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.

Keywords: sheaf with transfer, Gersten conjecture, equicharacteristic ring, Voevodsky motives, Gysin homomorphism, transfer, noetherian scheme, blow up.

UDC: 517.95

Received: 18.06.2015

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