Multiple zeta value cycles in low weight.

Abstract : In a recent work, the author has constructed two families of algebraic cycles in Bloch cycle algebra over the prjective line minus 3 points that are expected to correspond to multiple polylogarithms in one variable and have a good specialization at 1 related to multiple zeta values. This is a short presentation, by the way of toy examples in low weight ( 5), of this contruc- tion and could serve as an introduction to the general setting. Working in low weight also makes it possible to push ("by hand") the construction further. In particular, we will not only detail the construction of the cycle but we will also associate to these cycles explicit elements in the bar construction over the cycle algebra and make as explicit as possible the "bottow-left" coefficient of the Hodge realization periods matrix. That is, in a few relevant cases we will associated to each cycles an integral showing how the specialization at 1 is related to multiple zeta values. We will be particularly interested in a new weight 3 example .
Type de document :
Article dans une revue
Arithmeric, Geometry and Coding Theory - Contemporary mathematics, American Mathematical Society, 2015, Feynman amplitudes, periods and motives, 648, pp.203-247. <10.1090/conm/648/13004>
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-00787100
Contributeur : Ismaël Soudères <>
Soumis le : vendredi 28 février 2014 - 16:07:59
Dernière modification le : jeudi 25 février 2016 - 12:21:12
Document(s) archivé(s) le : mercredi 28 mai 2014 - 17:41:06

Fichiers

madrid-ISou.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Ismaël Soudères. Multiple zeta value cycles in low weight.. Arithmeric, Geometry and Coding Theory - Contemporary mathematics, American Mathematical Society, 2015, Feynman amplitudes, periods and motives, 648, pp.203-247. <10.1090/conm/648/13004>. <hal-00787100v2>

Partager

Métriques

Consultations de
la notice

142

Téléchargements du document

61