Embedding of category of twisted Chow-Witt correspondences into geometric stable $\A^1$-derived category over a field

Abstract

We introduce in this note the notion of the category of twisted Chow-Witt correspondences $CHW(k)$ over a field $k$ of characteristic different from $2$. Moreover, we show that over an infinite perfect field this category $CHW(k)$ admits a fully faithful embedding into the geometric stable $\A^1$-derived category $D_{\A^1,gm}(k)$ after taking $\Q$-localization. We also prove a conjecture of F. Morel about the rational splitting of stable $\A^1$-cohomology over an essentially smooth scheme $S$ over a field $k$ of $char(k)\ne 2$.

35 pages

References in corpus (3)

• Slices of hermitian K-theory and Milnor's conjecture on quadratic forms
• The 0-th stable A^1-homotopy sheaf and quadratic zero cycles
• Geometric models for higher Grothendieck-Witt groups in A1-homotopy theory