A Bogomolov property for curves modulo algebraic subgroups

Philipp Habegger

Bulletin de la Société Mathématique de France (2009)

  • Volume: 137, Issue: 1, page 93-125
  • ISSN: 0037-9484

Abstract

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Generalizing a result of Bombieri, Masser, and Zannier we show that on a curve in the algebraic torus which is not contained in any proper coset only finitely many points are close to an algebraic subgroup of codimension at least 2 . The notion of close is defined using the Weil height. We also deduce some cardinality bounds and further finiteness statements.

How to cite

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Habegger, Philipp. "A Bogomolov property for curves modulo algebraic subgroups." Bulletin de la Société Mathématique de France 137.1 (2009): 93-125. <http://eudml.org/doc/272302>.

@article{Habegger2009,
abstract = {Generalizing a result of Bombieri, Masser, and Zannier we show that on a curve in the algebraic torus which is not contained in any proper coset only finitely many points are close to an algebraic subgroup of codimension at least $2$. The notion of close is defined using the Weil height. We also deduce some cardinality bounds and further finiteness statements.},
author = {Habegger, Philipp},
journal = {Bulletin de la Société Mathématique de France},
keywords = {heights; Bogomolov property; Zilber-Pink conjecture},
language = {eng},
number = {1},
pages = {93-125},
publisher = {Société mathématique de France},
title = {A Bogomolov property for curves modulo algebraic subgroups},
url = {http://eudml.org/doc/272302},
volume = {137},
year = {2009},
}

TY - JOUR
AU - Habegger, Philipp
TI - A Bogomolov property for curves modulo algebraic subgroups
JO - Bulletin de la Société Mathématique de France
PY - 2009
PB - Société mathématique de France
VL - 137
IS - 1
SP - 93
EP - 125
AB - Generalizing a result of Bombieri, Masser, and Zannier we show that on a curve in the algebraic torus which is not contained in any proper coset only finitely many points are close to an algebraic subgroup of codimension at least $2$. The notion of close is defined using the Weil height. We also deduce some cardinality bounds and further finiteness statements.
LA - eng
KW - heights; Bogomolov property; Zilber-Pink conjecture
UR - http://eudml.org/doc/272302
ER -

References

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