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Preserving the Homotopy Invariance of Presheaves with Witt-Transfers Under Nisnevich Sheafication

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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.

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References

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Authors and Affiliations

  1. St.Petersburg State University, St.Petersburg, Russia

    A. E. Druzhinin

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  1. A. E. Druzhinin
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Correspondence to A. E. Druzhinin.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 423, 2014, p. 0.

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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

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  • DOI: https://doi.org/10.1007/s10958-015-2512-4

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