On v-adic periods of t-motives

In this paper, we prove the equality between the transcendental degree of the field generated by the v-adic periods of a t-motive M and the dimension of the Tannakian Galois group for M, where v is a “finite” place of the rational function field over a finite field. As an application, we prove the algebraic independence of certain “formal” polylogarithms.