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.
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Ishai Dan-Cohen, Tomer Schlank, Rational motivic path spaces and Kim’s relative unipotent section conjecture. Rend. Sem. Mat. Univ. Padova (2022), published online firstDOI 10.4171/RSMUP/97