A relative basis for mixed Tate motives over the projective line minus three points - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2013

A relative basis for mixed Tate motives over the projective line minus three points

Résumé

In a previous work, the author have built two families of distinguished algebraic cycles in Bloch-Kriz cubical cycle complex over the projective line minus three points. The goal of this paper is to show how these cycles induce well-defined elements in the $\HH^0$ of the bar construction of the cycle complex and thus generated comodules over this $\HH^0$, that is a mixed Tate motives as in Bloch and Kriz construction. In addition, it is shown that out of the two families only ones is needed at the bar construction level. As a consequence, the author obtains that one of the family gives a basis of the tannakian coLie coalgebra of mixed Tate motives over $\ps$ relatively to the tannakian coLie coalgebra of mixed Tate motives over $\Sp(\Q)$. This in turns provides a new formula for Goncharov motivic coproduct, which arise explicitly as the coaction dual to Ihara action by special derivations.
Fichier principal
Vignette du fichier
bar-basetext.pdf (385.07 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-00914982 , version 1 (06-12-2013)
hal-00914982 , version 2 (16-12-2014)
hal-00914982 , version 3 (28-12-2014)

Identifiants

Citer

Ismaël Soudères. A relative basis for mixed Tate motives over the projective line minus three points. 2013. ⟨hal-00914982v2⟩
86 Consultations
271 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More