Periods of Mixed Tate Motives, Examples,

International audienceOne hopes that theℚ-algebra of periods of mixed Tate motivesover Specℤis generated by values of iterated integrals onℙ1(ℂ)∖{0,1,∞}of sequences of one-forms푑푧푧and푑푧푧−1from→01 to→10. These numbers are alsocalled multiple zeta values. In this note, assuming motivic formalism, we givea proof, that theℚ-algebra of periods of mixed Tate motives over Specℤisgenerated by linear combinations with rational coefficients of iterated integralsonℙ1(ℂ)∖{0,1,−1,∞}of sequences of one-forms푑푧푧,푑푧푧−1and푑푧푧+1from→01to→10,which are unramified everywhere. The main subject of the paper ishowever the푙-adic Galois analogue of the above result. We shall also discusssome other examples in the푙-adic Galois settin