Abstract
Andrew Ogg’s mathematical viewpoint has inspired an increasingly
broad array of results and conjectures. His results and conjectures have
earmarked fruitful turning points in our subject, and his influence has been
such a gift to all of us. Ogg’s celebrated torsion conjecture—as it relates to
modular curves—can be paraphrased as saying that rational points (on the
modular curves that parametrize torsion points on elliptic curves) exist if and
only if there is a good geometric reason for them to exist. We give a survey of
Ogg’s torsion conjecture and the subsequent developments in our understanding
of rational points on modular curves over the last fifty years
broad array of results and conjectures. His results and conjectures have
earmarked fruitful turning points in our subject, and his influence has been
such a gift to all of us. Ogg’s celebrated torsion conjecture—as it relates to
modular curves—can be paraphrased as saying that rational points (on the
modular curves that parametrize torsion points on elliptic curves) exist if and
only if there is a good geometric reason for them to exist. We give a survey of
Ogg’s torsion conjecture and the subsequent developments in our understanding
of rational points on modular curves over the last fifty years
| Original language | English |
|---|---|
| Article number | 2 |
| Pages (from-to) | 235–268 |
| Number of pages | 34 |
| Journal | Bulletin of the American Mathematical Society |
| Volume | 62 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 12 Feb 2025 |