Mixed Tate motives over $\Z$

Abstract

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 $n_i\in \{2,3\}$