Explicit arithmetic intersection theory and computation of N\'eron-Tate heights
Number Theory
2019-04-04 v2
Abstract
We describe a general algorithm for computing intersection pairings on arithmetic surfaces. We have implemented our algorithm for curves over , and we show how to use it to compute regulators for a number of Jacobians of smooth plane quartics, and to numerically verify the conjecture of Birch and Swinnerton-Dyer for the Jacobian of the split Cartan curve of level 13, up to squares.
Cite
@article{arxiv.1809.06791,
title = {Explicit arithmetic intersection theory and computation of N\'eron-Tate heights},
author = {Raymond van Bommel and David Holmes and J. Steffen Müller},
journal= {arXiv preprint arXiv:1809.06791},
year = {2019}
}