Rigidity theorem for presheaves with Witt-transfers

Abstract

The rigidity theorem for homotopy invariant presheaves with Witt-transfers on the category of smooth affine varieties over a field $k$ with characteristic not equal to 2 is proved. Namely for such a presheaf $\mathcal F$ the isomorphism $\mathcal F(U)\simeq \mathcal F(x)$ where $U$ is henseliation of a variety at smooth closed point with separable residue field (over $k$) is proved. The rigidity for presheaves $W^i(X\times -)$ where $X$ is smooth variety and $W^i(-)$ are derived Witt-groups ($i\in \mathbb Z/4\mathbb Z$) follows as corollary.