Un cadre explicite pour les polylogarithmes multiples p-adiques et les multizêtas p-adiques

We define an explicit framework, involving sums of series, for p-adic multiple polylogarithms twisted by Frobenius, and for p-adic multiple zeta values. This framework is made of two types of combinatorial tools: operations related to the fundamental group of P1\{0,1,∞}, which enable us reduce ourselves to the computation of "elementary" regularized iterated integrals, and the p-adic computation of each such elementary iterated integral. The explicit formulae that are obtained imply non-optimal bounds on the valuation of p-adic multiple zeta values. This is a summary of the paper [6].