Periods of 1-motives and transcendence.
type: Item
instance of: scholarly article
title: Periods of 1-motives and transcendence.
zbMATH Open document ID: 1067.11041
DOI: 10.1016/S0022-314X(02)00002-1
author: Cristiana Bertolin
published in: Journal of Number Theory
publication date: 2003-04-02T00:00:00Z
review text: A number of recent speculations deal with the open problem of finding all algebraic relations between periods [\textit{M. Kontsevich,} and \textit{D. Zagier}, B. Engquist (ed.) et al., Mathematics unlimited - 2001 and beyond. Berlin: Springer, 771--808 (2001; Zbl 1039.11002)]. A far reaching statement, generalizing previous conjectures by Schanuel and Grothendieck, has been proposed by \textit{Y. André} [Quelques conjectures de transcendance issues de la géométrie algébrique, Institut Mathématique de Jussieu, preprint 121 (1997)]. The author specializes André's conjecture to \(1\)-motives and shows that it is equivalent to a statement which she calls the elliptico-toric conjecture. She produces a number of special cases involving the classical exponential function, elliptic Weierstraß\ \(\wp\) and \(\zeta\) functions, elliptic integrals and the modular invariant.
reviewed by: Michel Waldschmidt
Mathematics Subject Classification ID: 11J95
Mathematics Subject Classification ID: 11G05
Mathematics Subject Classification ID: 11J81
zbMATH DE Number: 1891439
zbMATH Keywords: Transcendence, algebraic independence, transcendence degree, Schanuel's conjecture, periods, \(1\)-motives, Grothendieck conjecture, de Rham cohomology, Mumford-Tate groups
MaRDI profile type: Publication
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full work available at URL: s0022-314x(02)00002-1
OpenAlex ID: W2035100180
description: scientific article; zbMATH DE number 1891439