Elliptic Curves Retaining Their Rank in Finite Extensions and Hilbert’s Tenth Problem for Rings of Algebraic Numbers
نویسنده
چکیده
Using Poonen’s version of “weak vertical method” we produce new examples of “large” and “small” rings of algebraic numbers (including rings of integers) where Z and/or the ring of integers of a subfield are existentially definable and/or where the ring version of Mazur’s conjecture on topology of rational points does not hold.
منابع مشابه
Rings of Algebraic Numbers in Infinite Extensions of Q and Elliptic Curves Retaining Their Rank
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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تاریخ انتشار 2006