Double mélange des multizêtas finis et multizêtas symétrisés

We interpret a conjecture on finite multizetas, due to Kaneko and Zagier, in terms of the De Rham fundamental groupoid ΠDR(P1−{0,1,∞}). We call the numbers that appear in this conjecture symmetrized multizetas. We show that finite multizetas and symmetrized multizetas satisfy the same variant of the double shuffle relations. We show that symmetrized multizetas satisfy a variant of certain associator relations, interpreting geometrically a result of Hoffman on finite multizetas. This is a preamble to a larger study of symmetrized multizetas and finite multizetas.