Small points and free abelian groups

Grizzard, Robert and Habegger, Philipp and Pottmeyer, Lukas. (2015) Small points and free abelian groups. International mathematics research notices, 20. pp. 10657-10679.

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Official URL: http://edoc.unibas.ch/39570/

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Let F be an algebraic extension of the rational numbers and E an elliptic curve defined over some number field contained in F. The absolute logarithmic Weil height, respectively, the Néron–Tate height, induces a norm on F∗ modulo torsion, respectively, on E(F) modulo torsion. The groups F∗ and E(F) are free abelian modulo torsion if the height function does not attain arbitrarily small positive values. In this paper, we prove the failure of the converse to this statement by explicitly constructing counterexamples.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Zahlentheorie (Habegger)
UniBasel Contributors:Pottmeyer, Lukas and Habegger, Philipp
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Hindawi Publ. Corp.
Note:Publication type according to Uni Basel Research Database: Journal article
Identification Number:
Last Modified:30 Jun 2016 10:59
Deposited On:17 May 2016 09:14

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