Open AccessGERSTEN COMPLEX FOR SHEAVES WITH TRANSFERS FOR NOETHERIAN SCHEMES
Author(s) -
A.A. Mingazov
Publication year - 2015
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2015-21-6-98-101
Subject(s) - noetherian , ring (chemistry) , conjecture , noetherian ring , mathematics , pure mathematics , algebra over a field , chemistry , finitely generated abelian group , organic chemistry
V. Voevodsky introduced Gersten complex for sheaves with transfers in one of the rst 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 eld 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 dened 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 eld k . This generalises Voevodsky’s result.