We determine the stable cohomology groups ($$H_S^i\left({𝔄}_n,\mathbb{Z}/\phantom{{𝔄}_n,\mathbb{Z}p\mathbb{Z}}p\mathbb{Z}\right)$$ of the alternating groups $${𝔄}_n$$ for all integers n and i, and all odd primes p.

Using the flatification by blow-up result of Raynaud and Gruson, we obtain new results for submersive and subtrusive morphisms. We show that universally subtrusive morphisms, and in particular universally open morphisms, are morphisms of effective descent for the fibered category of étale morphisms. Our results extend and supplement previous treatments on submersive morphisms by Grothendieck, Picavet and Voevodsky. Applications include the universality of geometric quotients and the elimination...

Dans cette note, nous montrons que la suite spectrale du coniveau associée à un spectre motivique sur un corps parfait coïncide avec sa suite spectrale d’hypercohomologie pour la t-structure homotopique.