• Corpus ID: 247793180

Unlikely and just likely intersections for high dimensional families of elliptic curves

@inproceedings{Asvin2022UnlikelyAJ,
  title={Unlikely and just likely intersections for high dimensional families of elliptic curves},
  author={G Asvin},
  year={2022}
}

• G. Asvin
• Published 30 March 2022
• Mathematics

Given two varieties V , W in the n-fold product of modular curves, we answer affirmatively a question (formulated by Shou-Wu Zhang’s AIM group) on whether the set of points in V that are Hecke translations of some point on W is dense in V . We need to make some (necessary) assumptions on the dimensions of V , W but for instance, when V is a divisor and W is a curve, no further assumptions are needed. We also examine the necessity of our assumptions in the case of unlikely intersections and show that, contrary to exceptions, two curves in a high dimensional space over a finite field can intersect infinitely often up to Hecke translations.