On $l$-adic iterated integrals, III. Galois actions on fundamental groups

Abstract

We continue to study $l$-adic iterated integrals introduced in the first part. We shall calculate explicitly $l$-adic logarithm and $l$-adic polylogarithms. Next we shall use these results to study Galois representations on the fundamental group of $\mathbf{B}P^{1}_{\overline{\mathbf{Q}(\mu_{n})}} \setminus \{ 0, \mu_{n} , \infty \}$.