Algebra Seminar

Let p be a prime and V be a finite-dimensional Q_p-vector space equipped with a continuous action of G, the absolute Galois group of Q. Fontaine and Mazur conjectured that if the inertia at p acts on V through a finite quotient then G acts through a finite quotient. In this talk we will explain a proof of this conjecture for representations of "geometric origin". This means in particular that V arises in the p-adic cohomology of smooth projective varieties over Q.