Relative Bogomolov extensions
Robert Grizzard
Acta Arithmetica, Tome 168 (2015), p. 1-13 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:286067 
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     title = {Relative Bogomolov extensions},
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     language = {en},
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Robert Grizzard. Relative Bogomolov extensions. Acta Arithmetica, Tome 168 (2015) pp. 1-13. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa170-1-1/