TY - JOUR

T1 - Preserving the homotopy invariance of presheaves with witt-transfers under nisnevich sheafication

AU - Druzhinin, A. E.

N1 - Druzhinin, A.E. Preserving the Homotopy Invariance of Presheaves with Witt-Transfers Under Nisnevich Sheafication. J Math Sci 209, 555–563 (2015). https://doi.org/10.1007/s10958-015-2512-4

PY - 2015

Y1 - 2015

N2 - In the present paper, it is introduced a category Wor the objects of which are affine smooth varieties over a field k and morphisms are certain variants of finite correspondences. A presheaf of Abelian groups with Witt-transfers is by definition a presheaf of Abelian groups on the category Wor. The homotopy invariance of the Nisnevich sheaf associated with an arbitrary homotopy invariant presheaf with Witt-transfers is proved. To construct a category of Witt-motives one should prove the homotopy invariance of Nisnevich cohomology of an arbitrary homotopy invariant Nisnevich sheaf with Witt-transfers.

AB - In the present paper, it is introduced a category Wor the objects of which are affine smooth varieties over a field k and morphisms are certain variants of finite correspondences. A presheaf of Abelian groups with Witt-transfers is by definition a presheaf of Abelian groups on the category Wor. The homotopy invariance of the Nisnevich sheaf associated with an arbitrary homotopy invariant presheaf with Witt-transfers is proved. To construct a category of Witt-motives one should prove the homotopy invariance of Nisnevich cohomology of an arbitrary homotopy invariant Nisnevich sheaf with Witt-transfers.

KW - Abelian Group

KW - Smooth Variety

KW - Triangulate Category

KW - QUADRATIC SPACES

KW - Homotopy invariance

UR - http://www.scopus.com/inward/record.url?scp=84943361288&partnerID=8YFLogxK

U2 - 10.1007/s10958-015-2512-4

DO - 10.1007/s10958-015-2512-4

M3 - Article

AN - SCOPUS:84943361288

VL - 209

SP - 555

EP - 563

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 4

M1 - A006

ER -