P -adic multiple zeta values II. Tannakian interpretations

Abstract

We establish a Tannakian formalism of p-adic multiple polylogarithms and p-adic multiple zeta values introduced in our previous paper via a comparison isomorphism between a de Rham fundamental torsor and a rigid fundamental torsor of the projective line minus three points and also discuss its Hodge and étale analogues. As an application we give a way to erase log poles of p-adic multiple polylogarithms and introduce overconvergent p-adic multiple polylogarithms which might be p-adic multiple analogue of Zagier's single-valued complex polylogarithms.