Periods and the conjectures of Grothendieck and Kontsevich-Zagier
type: Item
instance of: scholarly article
title: Periods and the conjectures of Grothendieck and Kontsevich-Zagier
zbMATH Open document ID: 1306.14006
author: Joseph Ayoub
published in: European Mathematical Society Newsletter
publication date: 2014-10-10T00:00:00Z
reviewed by: Michel Waldschmidt
Mathematics Subject Classification ID: 14F42
Mathematics Subject Classification ID: 14F40
Mathematics Subject Classification ID: 11S20
Mathematics Subject Classification ID: 14C15
Mathematics Subject Classification ID: 14F25
zbMATH DE Number: 6353857
zbMATH Keywords: periods
zbMATH Keywords: cohomology
zbMATH Keywords: Grothendieck conjecture
zbMATH Keywords: conjecture of Kontsevich-Zagier
zbMATH Keywords: motives
zbMATH Keywords: relative motivic Galois group
MaRDI profile type: Publication
review text: The first part of this paper is an introduction to the periods, the conjecture of \textit{M. Kontsevich} and \textit{D. Zagier} [in: Mathematics unlimited -- 2001 and beyond. Berlin: Springer. 771--808 (2001; Zbl 1039.11002)], the conjecture of Grothendieck on the relation between the transcendence degree of fields of periods and the dimension of the motivic Galois group, the extension of Grothendieck's conjecture by \textit{Y. André} to base field of nonzero transcendence degree [Une introduction aux motifs. Motifs purs, motifs mixtes, périodes. Paris: Société Mathématique de France (2004; Zbl 1060.14001)], and the connection, due to Kontsevich, between these conjectures [\textit{A. Huber} and \textit{S. Müller-Stach}, ``On the relation between Nori motives and Kontsevich periods'', preprint, \url{arXiv:1105.0865}].NEWLINENEWLINEThe second part of this paper is devoted to the geometric version of the conjecture of Kontsevich-Zagier, of which the author has provided a proof [\textit{J. Ayoub}, Ann. Math. 181, No. 3, 905--992 (2015; \url{doi:10.4007/annals.2015.181.3.2})].
description: scientific article; zbMATH DE number 6353857