JournalsrsmupOnline First13 July 2022

Rational motivic path spaces and Kim’s relative unipotent section conjecture

  • Ishai Dan-Cohen

    Ben-Gurion University of the Negev, Be’er Sheva, Israel
  • Tomer Schlank

    Hebrew University of Jerusalem, Israel
Rational motivic path spaces and Kim’s relative unipotent section conjecture cover
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Abstract

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.

Cite this article

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

DOI 10.4171/RSMUP/97