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.