Mixed Tate motives over $\Z$

Understand

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 $\zeta(n_1,..., n_r)$ where $n_i\in \{2,3\}$.