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

2017/03/31 by Dan-Cohen, Ishai, Schlank, Tomer · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1703.10776

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.

Cited by

• The motivic fundamental groupoid at tangential basepoints

Related

• Morphisms of rational motivic homotopy types
• Groupes fondamentaux motiviques de Tate mixte
• The motivic fundamental group of the projective line minus three points and the theorem of Siegel
• The motivic fundamental group of the punctured projective line
• The motivic fundamental groupoid at tangential basepoints