Research Papers

Once again of an analogue of the fundamental Voevodsky theorem

I. A. Panin^a, D. N. Tyurin<sup>b

a</sup> St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
^b National Research University Higher School of Economics, Moscow

Abstract: Let $k$ be an infinite perfect field. Let $F$ be $\mathbb{A}^{1}$-invariant quasi-stable $\mathbb{Z}F_{\ast}$-presheaf on the category of $k$-smooth varieties. We prove that in this case Zariski sheaf $F_{Zar}$ coincides with Nisnevich sheaf $F_{\mathrm Nis}$. Moreover, for any $k$-smooth scheme $X\in Sm/k$ there are equalities $H^{n}_{\mathrm Zar}(X, F_{\mathrm Zar})=H^{n}_{\mathrm Nis}(X,F_{\mathrm Nis})$.

Keywords: presheaves, framed transfers, Voevodsky theorem.

Received: 02.10.2025