Triangulated category of effective Witt-motives DWM-eff(k)

الأصل · EN

The category of effective Witt-motives DWM-(k) with functor WM Smₖ→ DWM-(k) defining motives of smooth affine varieties for perfect field k, char k≠ 2 is constructed. In the construction Voevodsky-Suslin method is applyed to a category of Witt-correspondence between affine smooth varieties WCorₖ that morphisms are defined by class in Witt-group of quadratic space (P,qₚ) with P being k[X× Y]-module finitely generated projective over k[X] and qₚ P→ Homₖ[ₓ](P,k[X]) being k[X× Y]-liner isomorphism. And the natural isomorphism HomDWM-eff(k)(WM(X),F[i]) ≃ HⁱNis(X,F) for any smooth affine X and homotopy invariant Nisnevich sheave F with Witt-transfers (that is presheave on the category WCorₖ such that its restriction on the category Smₖ is a sheave) is proved.