Let $\overline{ k}$ be a fixed algebraic closure of $k$. When the finite place $v$ is of degree one, we show that all $\overline{ k}$-linear relations among $v$-adic Carlitz multiple polylogarithms at algebraic points arise from $k$-linear relations among these values of the same weight. As an application, we establish a function field analogue of Furusho-Yamashita's conjecture for $v$-adic multiple zeta values whenever the degree of the place $v$ is one.
Categories: math.NT