Rational motivic path spacesand Kim’s relative unipotent section conjecture

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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.

Original languageEnglish
Pages (from-to)117-172
Number of pages56
JournalRendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova
StatePublished - 1 Jan 2022


  • motivic homotopy
  • nonabelian Chabauty
  • Rational homotopy
  • rational points
  • unipotent fundamental group

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Mathematical Physics
  • Geometry and Topology


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