Preserving the homotopy invariance of presheaves with Witt-transfers under Nisnevich sheafication. (English. Russian original) Zbl 1349.14058
J. Math. Sci., New York 209, No. 4, 555-563 (2015); translation from Zap. Nauchn. Semin. POMI 423, 113-125 (2014).
Summary: 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.
MSC:
| 14F05 | Sheaves, derived categories of sheaves, etc. (MSC2010) |
| 18E30 | Derived categories, triangulated categories (MSC2010) |
References:
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| [2] | P. Balmer, “Witt groups,” in: Handbook of K-Theory, Vol. 2, Springer, Berlin (2005), pp. 539-576. · Zbl 1115.19004 |
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| [7] | A. Druzhinin, “The preservation of homotopy invariance of presheaves with <Emphasis Type=”Italic“>Witttransfers under Nisnevich sheafication,” POMI Preprint No. 8 (2014). · Zbl 1349.14058 |
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