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

2007/05/30 by Alexandra Shlapentokh, Shlapentokh, Alexandra · 1 citation
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Algebraic and Geometric Analysis #Cryptography and Residue Arithmetic

paper · pdf · doi:10.48550/arxiv.0705.4324

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.

Cited by

• Using Indices of Points on an Elliptic Curve to Construct A Diophantine Model of \Z and Define \Z Using One Universal Quantifier in Very Large Subrings of Number Fields, Including \Q

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