Rings of Algebraic Numbers in Infinite Extensions of Q and Elliptic Curves Retaining Their Rank
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🧮 math.NT
math.LO
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extensionsinfiniteringscurvesellipticnumberssomealgebraic
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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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