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Relative Bogomolov extensions
Robert Grizzard
Acta Arithmetica
(2015)
- Volume: 170, Issue: 1, page 1-13
- ISSN: 0065-1036
A subfield K ⊆ ℚ̅ has the Bogomolov property if there exists a positive ε such that no non-torsion point of has absolute logarithmic height below ε. We define a relative extension L/K to be Bogomolov if this holds for points of . We construct various examples of extensions which are and are not Bogomolov. We prove a ramification criterion for this property, and use it to show that such extensions can always be constructed if some rational prime has bounded ramification index in K.
Robert Grizzard. "Relative Bogomolov extensions." Acta Arithmetica 170.1 (2015): 1-13. <http://eudml.org/doc/286067>.
@article{RobertGrizzard2015,
abstract = {A subfield K ⊆ ℚ̅ has the Bogomolov property if there exists a positive ε such that no non-torsion point of $K^\{×\}$ has absolute logarithmic height below ε. We define a relative extension L/K to be Bogomolov if this holds for points of $L^\{×\}∖K^\{×\}$. We construct various examples of extensions which are and are not Bogomolov. We prove a ramification criterion for this property, and use it to show that such extensions can always be constructed if some rational prime has bounded ramification index in K.},
author = {Robert Grizzard},
journal = {Acta Arithmetica},
keywords = {Bogomolov property; heights; infinite algebraic extensions},
language = {eng},
number = {1},
pages = {1-13},
title = {Relative Bogomolov extensions},
url = {http://eudml.org/doc/286067},
volume = {170},
year = {2015},
}
TY - JOUR
AU - Robert Grizzard
TI - Relative Bogomolov extensions
JO - Acta Arithmetica
PY - 2015
VL - 170
IS - 1
SP - 1
EP - 13
AB - A subfield K ⊆ ℚ̅ has the Bogomolov property if there exists a positive ε such that no non-torsion point of $K^{×}$ has absolute logarithmic height below ε. We define a relative extension L/K to be Bogomolov if this holds for points of $L^{×}∖K^{×}$. We construct various examples of extensions which are and are not Bogomolov. We prove a ramification criterion for this property, and use it to show that such extensions can always be constructed if some rational prime has bounded ramification index in K.
LA - eng
KW - Bogomolov property; heights; infinite algebraic extensions
UR - http://eudml.org/doc/286067
ER -
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