Bloch cycles complex over the projective line minus 3 points

We will describe, by means of Bloch and Kriz's approach, the coLie algebra of mixed Tate motives over P^{^1} minus three points in terms of explicit algebraic cycles. In particular, to do so, we construct algebraic cycles corresponding to multiple polylogarithms with a specialization at the point 1 corresponding to multiple zeta values.

We will insist on the geometric situation and present the approach and the difficulties through the example of polylogarithms and through some low weight examples.