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arXiv · 0705.4324

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

Alexandra Shlapentokh
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Abstract

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.

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BibTeXRIS

Alexandra Shlapentokh. 2007-05-30. Rings of Algebraic Numbers in Infinite Extensions of $\Q$ and Elliptic Curves Retaining Their Rank. https://arxiv.org/abs/0705.4324

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