Étale motives of geometric origin

Abstract

Over qcqs finite-dimensional schemes, we prove that étale motives of geometric origin can be characterised by a constructibility property which is purely categorical, giving a full answer to the question "Do all constructible étale motives come from geometry?" which dates back to Cisinski and Déglise's work. We also show that they afford the continuity property and satisfy h-descent and Milnor excision.

Reorganisation of the proof of the main theorem, the ring of coefficients now has to be ind-regular. 14 pages, comments welcome!