Carlo Pagano, Concordia University
Reconstructing curves from their Galois set of points
Mazur—Rubin asked to what extent one can reconstruct a curve C over a number field K from its set of points over bar(K), viewed as a Galois set. They asked the same question specifically about the set of fields where C acquires new points and gave evidence for a positive answer for curves of genus 0. In this talk we will present upcoming work with Zev Klagsbrun where we provide a positive answer for a generic pair of elliptic curves with full 2-torsion over a number field. The method of proof uses the combination of additive combinatorics and descent introduced in joint work of the speaker and Koymans in 2024. I will overview several other recent results obtained, by a number of authors, with that method.
MC 5479