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arXiv:0705.4324 [math.NT]AbstractReferencesReviewsResources

Rings of Algebraic Numbers in Infinite Extensions of $\Q$ and Elliptic Curves Retaining Their Rank

Alexandra Shlapentokh

Published 2007-05-30Version 1

We show that elliptic curves whose Mordell-Weil groups are finitely generated over some infinite extensions of $\Q$, can be used to show the Diophantine undecidability of the rings of integers and bigger rings contained in some infinite extensions of rational numbers.

Categories: math.NT, math.LO
Subjects: 11U05, 11G05
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