Nisnevich sheafification of a homotopy invariant presheaf with transfers

Druzhinin, A.

doi:10.1090/spmj/1519

Nisnevich sheafification of a homotopy invariant presheaf with transfers
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by A. Druzhinin
Translated by: A. Druzhinin

St. Petersburg Math. J. 29 (2018), 863-886

DOI: https://doi.org/10.1090/spmj/1519

Published electronically: September 4, 2018

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Abstract:

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 $\mathcal F_{\mathrm {nis}}$ of a homotopy invariant presheave with Witt-transfers $\mathcal F$ is proved, and the Nisnevich cohomologies $H^i_{\mathrm {nis}}(U,\mathcal F_{\mathrm {nis}})$ are shown to be trivial for any $U\subset \mathbb A^1$ and $i>0$.

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