Rational motivic path spaces and Kim's relative unipotent Section conjecture (Q2697596)

Summary: We develop the foundations of commutative algebra objects in the category of motives, which we call ``motivic dga's.'' Works of White and Cisinski and Déglise provide us with a suitable model structure. This enables us to reconstruct the unipotent fundamental group of a pointed scheme from the associated augmented motivic dga and provides us with a factorization of Kim's relative unipotent section conjecture into several smaller conjectures with a homotopical flavor.