Abstract
We prove that the category of mixed Tate motives over $\mathbb{Z}$ is spanned by the motivic fundamental group of $\mathbb{P}^1$ minus three points. We prove a conjecture by M. Hoffman which states that every multiple zeta value is a $\mathbb{Q}$-linear combination of $\zeta(n_1,\ldots, n_r)$, where $n_i\in \{2,3\}$.
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