Tate motives and the fundamental group

2007/08/29 by Hélène Esnault, Esnault, Hélène, Marc Levine +1
Mathematics · #14C25 #19E15 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #K-Theory and Homology (math.KT) #math.AG #math.KT #msc:14C25 #msc:19E15

paper · pdf · doi:10.48550/arxiv.0708.4034

arxiv created 2007/08/29 · openalex publication_date 2007/08/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let k be a number field, and let S be a finite set of k-rational points of P¹. We relate the Deligne-Goncharov contruction of the motivic fundamental group of X:=P¹_k- S to the Tannaka group scheme of the category of mixed Tate motives over X.

Related

• Groupes fondamentaux motiviques de Tate mixte
• Derived Fundamental Groups for Tate Motives
• The motivic fundamental group of the punctured projective line
• A note on 1-motives
• On p-adic periods for mixed Tate motives over a number field