Heuristics for the arithmetic of elliptic curves
Number Theory
2017-12-04 v2 Algebraic Geometry
Abstract
This is an introduction to a probabilistic model for the arithmetic of elliptic curves, a model developed in a series of articles of the author with Bhargava, Kane, Lenstra, Park, Rains, Voight, and Wood. We discuss the theoretical evidence for the model, and we make predictions about elliptic curves based on corresponding theorems proved about the model. In particular, the model suggests that all but finitely many elliptic curves over have rank , which would imply that the rank is uniformly bounded.
Cite
@article{arxiv.1711.10112,
title = {Heuristics for the arithmetic of elliptic curves},
author = {Bjorn Poonen},
journal= {arXiv preprint arXiv:1711.10112},
year = {2017}
}
Comments
13 pages; submitted to the Proceedings of the 2018 ICM. Version 2 adds some references and corrects some typos