Fourier transform for étale motivic cohomology

Abstract

In the present article, we study the integral aspects of the Fourier transform of an abelian variety $A$ over a field $k$, using étale motivic cohomology, following the ideas and theory given by Moonen, Polishchuk and later by Beckman and de Gaay Fortman. We prove that there exists a PD-structure over the positive degree part of the étale Chow ring ${\text{CH}}_{>0}^{\text{eˊt}}(A)$ with respect to the Pontryagin product.