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arXiv · 1703.10776

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

Ishai Dan-Cohen·Tomer Schlank
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Abstract

We initiate a study of path spaces in the nascent context of "motivic dga's", under development in doctoral work by Gabriella Guzman. 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. Based on a conversation with Joseph Ayoub, we prove that the path spaces of the punctured projective line over a number field are concentrated in degree zero with respect to Levine's t-structure for mixed Tate motives. This constitutes a step in the direction of Kim's conjecture.

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Ishai Dan-Cohen, Tomer Schlank. 2017-03-31. Rational motivic path spaces and Kim's relative unipotent section conjecture. https://arxiv.org/abs/1703.10776

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