Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

Explicit arithmetic intersection theory and computation of Néron-Tate heights


Authors: Raymond van Bommel, David Holmes and J. Steffen Müller
Journal: Math. Comp. 89 (2020), 395-410
MSC (2010): Primary 14G40; Secondary 11G30, 11G50, 37P30
DOI: https://doi.org/10.1090/mcom/3441
Published electronically: May 17, 2019
Full-text PDF
View in AMS MathViewer New

Abstract | References | Similar Articles | Additional Information

Abstract: We describe a general algorithm for computing intersection pairings on arithmetic surfaces. We have implemented our algorithm for curves over $ \mathbb{Q}$, 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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2010): 14G40, 11G30, 11G50, 37P30

Retrieve articles in all journals with MSC (2010): 14G40, 11G30, 11G50, 37P30


Additional Information

Raymond van Bommel
Affiliation: Mathematisch Instituut, Universiteit Leiden, Postbus 9512, 2300 RA Leiden, Netherlands
Email: raymondvanbommel@gmail.com

David Holmes
Affiliation: Mathematisch Instituut, Universiteit Leiden, Postbus 9512, 2300 RA Leiden, Netherlands
Email: d.s.t.holmes@math.leidenuniv.nl

J. Steffen Müller
Affiliation: Bernoulli Institute, University of Groningen, Nijenborgh 9, 9747 AG Groningen, Netherlands
Email: steffen.muller@rug.nl

DOI: https://doi.org/10.1090/mcom/3441
Received by editor(s): September 27, 2018
Received by editor(s) in revised form: February 11, 2019, and February 27, 2019
Published electronically: May 17, 2019
Article copyright: © Copyright 2019 American Mathematical Society