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Independence of rational points on twists of a given curve

Title data

Stoll, Michael:
Independence of rational points on twists of a given curve.
In: Compositio Mathematica. Vol. 142 (September 2006) Issue 5 . - pp. 1201-1214.
ISSN 1570-5846
DOI: https://doi.org/10.1112/S0010437X06002168

Abstract in another language

In this paper, we study bounds for the number of rational points on twists C' of a fixed curve C over a number field K, under the condition that the group of K-rational points on the Jacobian J' of C' has rank smaller than the genus of C'. The main result is that with some explicitly given finitely many possible exceptions, we have a bound of the form 2r+c, where r is the rank of J'(K) and c is a constant depending on C. For the proof, we use a refinement of the method of Chabauty-Coleman: the main new ingredient is to use it for an extension field of K_v, where v is a place of bad reduction for C'.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: rational points on curves; twists; Chabauty-Coleman method
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: No
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 03 Feb 2015 07:03
Last Modified: 14 Jan 2016 12:05
URI: https://eref.uni-bayreuth.de/id/eprint/6221