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

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    Abstract

    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.

    Original languageEnglish
    Article numberA006
    Pages (from-to)555-563
    Number of pages9
    JournalJournal of Mathematical Sciences (United States)
    Volume209
    Issue number4
    Early online date1 Aug 2015
    DOIs
    StatePublished - 2015

    Scopus subject areas

    • Statistics and Probability
    • Mathematics(all)
    • Applied Mathematics

    Keywords

    • Abelian Group
    • Smooth Variety
    • Triangulate Category
    • QUADRATIC SPACES
    • Homotopy invariance

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