Chow Künneth decomposition for étale motives

Abstract

In the present article we define an integral analogue of Chow-Künneth decomposition for étale motives. By using families of conservative functors we are able to establish a decomposition of the étale motive of commutative group schemes over a base and we relate to an integral étale Chow-Künneth decomposition of abelian varieties. For a projective variety $X$ of dimension $d$ over an algebraically closed field, we construct integral sub-motives $h_{\text{eˊt}}^1(X)$ and $h_{\text{eˊt}}^{2d-1}(X)$ of the motive $h_{\text{eˊt}}(X)$.