Mixed Tate motives over $\Z$

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

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