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Duality on tori and multiplicative dependence relations

Part of: Abelian varieties and schemes

Published online by Cambridge University Press:  09 April 2009

Daniel Bertrand
Daniel Bertrand
Affiliation:
Université de Paris VI Institut de Mathématiques, T. 46, C. 247 4, Place Jussieu 75 252 Paris Cédex 05France e-mail: bertrand@math.jussieu.fr
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Abstract

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In this paper, we give multihomogeneous estimates for the group of relations linking multiplicatively dependent algebraic numbers. In the process, we raise a question in the style of Lehmer's problem, concerning multidimensional covolumes in the lattice of units. The proofs are based on the Brill-Gordan duality theorem on orthogonal lattices, and the paper closes with an algebraic version of the theorem, concerning orthogonal abelian subvarieties of an arbitrarily polarized abelian variety.

Keywords

geometry of numbersregulatorsabelian varieties.

MSC classification

Secondary: 14K05: Algebraic theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 62 , Issue 2 , April 1997 , pp. 198 - 216
Copyright
Copyright © Australian Mathematical Society 1997

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