The generalized Fermat equation x3+y4+z5=0

Samir Siksek (Warwick Univ.)

This talk is based on joint work with Michael Stoll (Bayreuth). The equation of the title was suggested by Zagier as the next case of the Generalized Fermat Conjecture. Work of Edwards reduces this equation to the determination of rational points on 49 hyperelliptic curves of genus 14. Standard methods for determining the rational points fail on many of these curves. We describe a new technique which we call 'partial descent' that succeeds in completing the determination of rational points on these curves. We deduce that the only solutions in coprime integers x, y, z satisfy xyz=0.

Marti 15 Iunie, ora 11:00