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Raphaël Ruimy - Étale motives of geometric origin.

In "Étale motives", Cisinski and Déglise defined two finiteness conditions on étale motives: motives that come from geometry and motives that are dualisable over a stratification. In a joint paper with S. Tubach, we showed that both conditions give the same category. To prove this, we first reduce to the case of fields by use the six functors and continuity, then we use some results on Artin motives and a result of Balmer and Gallauer on representations of finite groups. We also prove that geometric étale motives satisfy Milnor excision. I will then explain some applications to Nori motives with integral coefficients and arc-descent for them.