### Construction inconditionnelle de groupes de Galois motiviques, by Yves André and Bruno Kahn

We also study the specialisation of numerical motives and the behaviour of motivic Galois group by specialisation. If K is a complete discrete valuation field with residue field k, choose a pair of compatible classical Weil cohomologies (H_K,H_k). Let Mot_{H_K,b}^* be the full subcategory of Mot^*_{H_K} consisting of motives with good reduction, Mot_{\num,b}^* its full image in Mot_\num^*, and G_{H_K}^b the quotient of G_{H_K} corresponding to Mot_{\num,b}^*. Then we construct a cospecialisation" homomorphism G_{H_k}\to G_{H_K}^b, compatible with the specialisation of correspondences and well-defined up to inner automorphism.

Yves André <andre@math.jussieu.fr>
Bruno Kahn <kahn@math.jussieu.fr>