Descent on elliptic curves and Hilbert’s tenth problem

Eisenträger, Kirsten; Everest, Graham

doi:10.1090/S0002-9939-08-09740-2

Descent on elliptic curves and Hilbert’s tenth problem
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by Kirsten Eisenträger and Graham Everest PDF

Proc. Amer. Math. Soc. 137 (2009), 1951-1959 Request permission

Abstract:

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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