On some negative motivic homology groups

Abstract

For an arbitrary separated scheme $X$ of finite type over a finite field ${\mathbb{F}}_q$ and an integer $j=-1,-2,$ we prove under the assumption of resolution of singularities, that the two groups $H_{-1}(X,\mathbb{Z}(j))$ and $H_{-1}({\pi }_0(X),\mathbb{Z}(j))$ are canonically isomorphic. This gives an explicit computation of $H_{-1}(X,\mathbb{Z}(j)).$

Same as the published version except for a minor editorial difference

References in corpus (2)

• Cancellation theorem
• On two higher Chow groups of schemes over a finite field