### L'algèbre de Hopf et le groupe de Galois motiviques d'un corps de caractéristique nulle, by Joseph Ayoub

We introduce a general formalism allowing one to associate to some monoidal
functors a Hopf algebra in the target category. This formalism is applied to
the Betti realization of Voevodsky's motives over a base field k endowed with
a complex embedding. We obtain in this way a Hopf algebra in the derived
category of Q-vector spaces. Using the comparison theorem of singular
cohomology with algebraic de Rham cohomology, we deduce that this Hopf algebra
has no homology in strictly negative degrees. Its zero degree homology is thus
a Hopf algebra in the usual sense and its spectrum is called the motivic Galois
group. We study different aspects of these motivic Hopf algebras and these
motivic Galois groups.

Joseph Ayoub <joseph.ayoub@math.uzh.ch>