Integral points on hyperelliptic curves
By Yann Bugeaud, Maurice Mignotte, Samir Siksek, Michael Stoll, Szabolcs Tengely. 2008
64 citations recorded by the source corpus.
Let C : Y-2 = a(n)X(n)+...+a(0) be a hyperelliptic curve with the ai rational integers, n >= 5, and the polynomial on the right- hand side irreducible. Let J be its Jacobian. We give a completely explicit upper bound for the integral points on the model C, provided we know at least one rational point on C and a Mordell Weil basis for J (Q). We also explain a powerful refinement of the Mordell - Weil sieve which, combined with the upper bound, is capable of determining all the integral points. Our method is illustrated by determining the integral points on the genus 2 hyperelliptic models Y-2 - Y = X-5 - X and (Y 2) = (X 5).
Subfields: Artificial Intelligence, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/492b6c6f3fd5b0b2c017b03f2821220d4f36329d
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Citations in the corpus
- Explicit Chabauty over number fields (2010, background): “, [Bruin and Elkies 2002; Bruin and Stoll 2008; 2010; Bugeaud et al. 2008], as well as the above sketch assume full knowledge of the Mordell–Weil group.”