Smoothness of the law of the supremum of the fractional Brownian motion

This is the published version, also available here: http://dx.doi.org/10.1214/ECP.v8-1079.This note is devoted to prove that the supremum of a fractional Brownian motion with Hurst parameter H∈(0,1) has an infinitely differentiable density on (0,∞). The proof of this result is based on the techniques of the Malliavin calculus