A note on ramification of the Galois representation on the fundamental group of an algebraic curve

Abstract

Abstract Let X be a smooth proper connected algebraic curve defined over an algebraic number field K. Let πl( X )l be the pro-l completion of the geometric fundamental group of X = X ⊗K K . Let p be a prime of K, which is coprime to l. Assuming that X has bad reduction at p and the Jacobian variety of X has good reduction at p , we describe the action of the inertia group I p on the quotient groups of π1( X )l by the higher commutator subgroups.