Abstract
This paper is a culmination of [CM21] on the study of multiple zeta values (MZV’s) over function fields in positive characteristic. For any finite place v of the rational function field k over a finite field, we prove that the v-adic MZV’s satisfy the same ¯ k-algebraic relations that their corresponding ∞-adic MZV’s satisfy. Equivalently, we show that the v-adic MZV’s form an algebra with multiplication law given by the q-shuffle product which comes from the ∞-adic MZV’s, and there is a well-defined ¯ k-algebra homomorphism from the ∞-adic MZV’s to the v-adic MZV’s.