Triangulated category of effective Witt-motives DWM^-_eff(k)

2016/01/20 by Andrei Druzhinin, Druzhinin, Andrei
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1601.05383

openalex publication_date 2016/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The category of effective Witt-motives DWM^-(k) with functor WM\colon Sm_k→ 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 WCor_k that morphisms are defined by class in Witt-group of quadratic space (P,q_P) with P being k[X× Y]-module finitely generated projective over k[X] and q_P\colon P→ Hom_k[X](P,k[X]) being k[X× Y]-liner isomorphism. And the natural isomorphism Hom_DWM^-_eff(k)(WM(X),\mathcal F[i]) ≃ Hⁱ_Nis(X,\mathcal F) for any smooth affine X and homotopy invariant Nisnevich sheave \mathcal F with Witt-transfers (that is presheave on the category WCor_k such that its restriction on the category Sm_k is a sheave) is proved.

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