Étale degree map and 0-cycles
Résumé
Using the triangulated category of & eacute;tale motives over a field k, for a smooth projective variety X over k, we define the group CH & eacute;t 0 (X) as an & eacute;tale analogue of 0-cycles. We study the properties of CH & eacute;t 0 (X) and give a description of the birational invariance of such a group. We define and present the & eacute;tale degree map using Gysin morphisms in & eacute;tale motivic cohomology and the & eacute;tale index as an analogue to the classical case. We give examples of smooth projective varieties over a field k without zero cycles of degree one but with & eacute;tale zero cycles of degree one, but this property is not always true as we give examples where the & eacute;tale degree map is not surjective.