On integrality of p-adic iterated integrals

The purpose of this paper is to prove integrality for certain p-adic iterated Coleman integrals. As underlying geometry we will take the complement of a divisor D⊂X with good reduction, where X is the projective line or an elliptic curve over the Witt vectors of a perfect characteristic p field. As a corollary we prove a lower bound for the valuations of p-adic multiple zeta values.