Small points on a multiplicative group and class number problem

Francesco Amoroso[1]

  • [1] Université de Caen Laboratoire de Mathématiques Nicolas Oresme, U.M.R. 6139 (C.N.R.S.) Campus II, BP 5186 F–14032 Caen Cedex

Journal de Théorie des Nombres de Bordeaux (2007)

  • Volume: 19, Issue: 1, page 27-39
  • ISSN: 1246-7405

Abstract

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Let V be an algebraic subvariety of a torus 𝔾 m n ↪ ℙ n and denote by V * the complement in V of the Zariski closure of the set of torsion points of V . By a theorem of Zhang, V * is discrete for the metric induced by the normalized height h ^ . We describe some quantitative versions of this result, close to the conjectural bounds, and we discuss some applications to study of the class group of some number fields.

How to cite

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Amoroso, Francesco. "Small points on a multiplicative group and class number problem." Journal de Théorie des Nombres de Bordeaux 19.1 (2007): 27-39. <http://eudml.org/doc/249982>.

@article{Amoroso2007,
abstract = {Let $V$ be an algebraic subvariety of a torus $\{\mathbb\{G\}\}_m^n\hookrightarrow \{\mathbb\{P\}\}^n$ and denote by $V^*$ the complement in $V$ of the Zariski closure of the set of torsion points of $V$. By a theorem of Zhang, $V^*$ is discrete for the metric induced by the normalized height $\hat\{h\}$. We describe some quantitative versions of this result, close to the conjectural bounds, and we discuss some applications to study of the class group of some number fields.},
affiliation = {Université de Caen Laboratoire de Mathématiques Nicolas Oresme, U.M.R. 6139 (C.N.R.S.) Campus II, BP 5186 F–14032 Caen Cedex},
author = {Amoroso, Francesco},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {Lehmer's problem; heights; class numbers; exponent of class group},
language = {eng},
number = {1},
pages = {27-39},
publisher = {Université Bordeaux 1},
title = {Small points on a multiplicative group and class number problem},
url = {http://eudml.org/doc/249982},
volume = {19},
year = {2007},
}

TY - JOUR
AU - Amoroso, Francesco
TI - Small points on a multiplicative group and class number problem
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2007
PB - Université Bordeaux 1
VL - 19
IS - 1
SP - 27
EP - 39
AB - Let $V$ be an algebraic subvariety of a torus ${\mathbb{G}}_m^n\hookrightarrow {\mathbb{P}}^n$ and denote by $V^*$ the complement in $V$ of the Zariski closure of the set of torsion points of $V$. By a theorem of Zhang, $V^*$ is discrete for the metric induced by the normalized height $\hat{h}$. We describe some quantitative versions of this result, close to the conjectural bounds, and we discuss some applications to study of the class group of some number fields.
LA - eng
KW - Lehmer's problem; heights; class numbers; exponent of class group
UR - http://eudml.org/doc/249982
ER -

References

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