Nisnevich sheafification of a homotopy invariant presheaf with transfers

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    The definitions of the category of finite Witt-correspondences and of a presheaf with Witt-transfers are given. The injectivity on the affine line, the excision isomorphism on the affine line, and the excision isomorphism for an étale morphism of curves are proved. The homotopy invariance of the Nisnevich sheafification Fnis of a homotopy invariant presheave with Witt-transfers F is proved, and the Nisnevich cohomologies Hnis i (U,Fnis) are shown to be trivial for any U ⊃ A1 and i > 0.

    Original languageEnglish
    Pages (from-to)863-886
    JournalSt. Petersburg Mathematical Journal
    Issue number6
    StatePublished - 1 Jan 2018

    Scopus subject areas

    • Analysis
    • Applied Mathematics
    • Algebra and Number Theory


    • Excision isomorphisms
    • Homotopy invariance
    • Presheaves with transfers
    • presheaves with transfers
    • excision isomorphisms


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