In this article, we construct étale realization functors defined on étale motives (without transfers) over a scheme X. Our construction is natural and relies on a relative rigidity theorem à la Suslin-Voevodsky that we will establish first. Then, we show that these realization functors are compatible with Grothendieck operations and the "nearby cycles" functors. Along the way, we will prove a number of properties concerning étale motives.
Joseph Ayoub <firstname.lastname@example.org>