Mixed Tate motivic fundamental groups. (Groupes fondamentaux motiviques de Tate mixte.) (French) Zbl 1084.14024
The paper under review studies the motivic unipotent fundamental group of an affine rational curve. It follows Deligne’s previous treatment of the étale realisation. The new ingredients are realisations (attributed to Beilinson) of universal unipotent bundles as cohomology of schemes, and Voevodsky’s construction of a derived category of motives. The latter allows to define repeated extensions of Tate-motives. Finally the authors study the automorphisms of this unipotent group.
Reviewer: Gerd Faltings (Bonn)
MSC:
| 14F42 | Motivic cohomology; motivic homotopy theory |
| 14G10 | Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) |
| 11G55 | Polylogarithms and relations with \(K\)-theory |
| 19F27 | Étale cohomology, higher regulators, zeta and \(L\)-functions (\(K\)-theoretic aspects) |
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