Algebra structure of multiple zeta values in positive characteristic

On Thakur’s basis conjecture for multiple zeta values in positive characteristic

“…By [13,Thm. 1.2.2], there is a natural k-linear map from (∞-adic) MZV's to v-adic MZV's, and it was further shown in [11] that the map is indeed an algebra homomorphism with kernel containing the ideal generated by 𝜁 𝐴 (𝑞 − 1) since 𝜁 𝐴 (𝑞 − 1) 𝑣 = 0 by [19]. As a consequence of Theorem 1.5, we have the following upper bound result for v-adic MZV's.…”