Descent on Elliptic Curves and Hilbert's Tenth Problem

Details Descent on Elliptic Curves and Hilbert's Tenth Problem Descent on Elliptic Curves and Hilbert's Tenth Problem

2007-07-10

arxiv.org/abs/0707.1485v5

Mathematics

Number Theory

Second author added. Paper now accepted by Proc AMS

Scientific paper

Descent via an isogeny on an elliptic curve is used to construct two subrings
of the field of rational numbers, which are complementary in a strong sense,
and for which Hilbert's Tenth Problem is undecidable. This method further
develops that of Poonen, who used elliptic divisibility sequences to obtain
undecidability results for some large subrings of the rational numbers.

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