Periods of mixed Tate motives. Examples, l-adic Galois side.

The iterated integrals from 01 to 10 in sequences of one-forms $dz/z$ and $dz/(z-1)$ are periods of mixed Tate motives over Spec Z. The obvious question is if in this way we shall get all periods of mixed Tate motives over Spec Z. We shall construct an l-adic Galois version of this problem and its generalization. We shall construct in the l-adic Galois setting all periods of mixed Tate motives (we call them coefficients) over Spec Z $[1/p]$, hence also over Spec Z, and also over Spec Z[i $\sqrt{p}$] (with $p=3(mod 4)$ in the last case). We shall use the action of $G_{Q(\mu_p)}$ on $pi_1(P^1_{\bar Q}(\{0,infty\}\cup \mu_p),{\overline 01})$, with $p$ a prime number.