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Quadratic Chabauty : p-adic heights and integral points on hyperelliptic curves

Title data

Balakrishnan, Jennifer S. ; Besser, Amnon ; Müller, Jan Steffen:
Quadratic Chabauty : p-adic heights and integral points on hyperelliptic curves.
In: Journal für die Reine und Angewandte Mathematik. Vol. 720 (November 2016) . - pp. 51-79.
ISSN 0075-4102
DOI: https://doi.org/10.1515/crelle-2014-0048

Project information

Project title:
Project's official titleProject's id
No informationKU 2359/2-1

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

We give a formula for the component at p of the p-adic height pairing of a divisor of degree 0 on a hyperelliptic curve. We use this to give a Chabauty-like method for finding p-adic approximations to p-integral points on such curves when the Mordell–Weil rank of the Jacobian equals the genus. In this case we get an explicit bound for the number of such p-integral points, and we are able to use the method in explicit computation. An important aspect of the method is that it only requires a basis of the Mordell–Weil group tensored with ℚ.

Further data

Item Type: Article in a journal
Refereed: Yes
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 04 May 2017 09:57
Last Modified: 04 May 2017 09:57
URI: https://eref.uni-bayreuth.de/id/eprint/36943