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Rational points on hyperelliptic curves : recent developments

Title data

Stoll, Michael:
Rational points on hyperelliptic curves : recent developments.
In: Computeralgebra-Rundbrief. Vol. 54 (March 2014) . - pp. 10-13.
ISSN 0933-5994

Official URL: Volltext

Abstract in another language

We give an overview over recent results
concerning rational points on hyperelliptic
curves. One result says that ‘most’ hyperellip-
tic curves of high genus have very few ratio-
nal points. Another result gives a bound on the
number of rational points in terms of the genus
and the Mordell-Weil rank, provided the latter
is sufficiently small. The first result relies on
work by Bhargava and Gross on Selmer groups
of hyperelliptic Jacobians, and both results use
Chabauty’s method.

Further data

Item Type: Article in a journal
Refereed: No
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II > Chair Mathematics II - Univ.-Prof. Dr. Michael Stoll
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: 19 Feb 2015 12:58
Last Modified: 19 Feb 2015 12:58
URI: https://eref.uni-bayreuth.de/id/eprint/7227