On the structure of Multiple q-Zeta Values

In 2015, Bachmann \cite{Ba3} conjectured that the~$\text{Q}$-vector space~$\text{Zq}$ of (formal)~$q$-analogues of Multiple Zeta Values (\qmzv s) is spanned by a very particular set compared to known spanning sets. In this work, we prove that this conjecture is true for a subspace of~$\text{Zq}$ spanned by words satisfying some condition on their number of zeros and depth. According to this partial result, we give an explicit approach to the whole conjecture, based on particular~$\text{Q}$-linear relations among formal Multiple~$q$-Zeta Values which are implied by duality.