Yidi Wang, University of Waterloo
Local-global principles on stacky curves and its application in solving generalized Fermat equations.
The primitive solutions of certain generalized Fermat equations, i.e.,
Diophantine equations of the form Ax^p+By^q = Cz^r, can be studied as
integral points on certain stacky curves. In a recent paper by Bhargava and
Poonen, an explicit example of such a curve of genus 1/2 violating
local-global principle for integral points was given. However, a general
description of stacky curves failing the local-global principle is
unknown. In this talk, I will discuss our work on finding the primitive
solutions to equation of the form when (p, q, r) = (2,2,n) by studying local-global principles for integral points on stacky curves constructed from such equations.
The talk is based on a joint project with Juanita Duque-Rosero,
Christopher Keyes, Andrew Kobin, Manami Roy and Soumya Sankar.
MC 5417