A guide to (étale) motivic sheaves

Abstract

We recall the construction, following the method of Morel and Voevodsky, of the triangulated category of étale motivic sheaves over a base scheme. We go through the formalism of Grothendieck’s six operations for these categories. We mention the relative rigidity theorem. We discuss some of the tools developed by Voevodsky to analyze motives over a base field. Finally, we discuss some long-standing conjectures.