2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66595We define the category of mixed Tate motives over the ring of S-integers of a number field. We define the motivic fundamental group (made unipotent) of a unirational variety over a number field. We apply this to the study of the motivic fundamental group of the projective line punctured at zero, infinity and all N-th roots of unity.84 pages, v2: a transmission error correctedNumber TheoryAlgebraic Geometrytext