Galois action on fundamental groups and geometry of modular varieties

(Un exposé d'Alexander Goncharov au séminaire de théorie des nombres de Chevaleret le 9 février 2004)

Résumé :

  We will discuss some old and new results on the image of the absolute/motivic Galois group acting on the pro-$l$/motivic fundamental group of the multiplicative group without all $p$-th roots of unity, and their relationship with the geometry of certain level $p$ modular varieties for $GL_m(Z)$.