Rational motivic path spacesand Kim’s relative unipotent section conjecture

Ishai Dan-Cohen, Tomer Schlank

Research output: Contribution to journalArticlepeer-review


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

Bibliographical note

Publisher Copyright:
© 2022 Università degli Studi di Padova Published by EMS Press.


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


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