Journal title
Monatshefte fur Mathematik
DOI
10.1007/s00605-014-0711-6
Issue
2
Volume
176
Last updated
2023-06-24T14:49:57.457+01:00
Page
197-218
Abstract
Given number fields L ⊃ K, smooth projective curves C defined over L and B defined over K, and a non-constant L-morphism h: C→BL, we denote by Ch the curve defined over K whose K-rational points parametrize the L-rational points on C whose images under h are defined over K. We compute the geometric genus of the curve Ch and give a criterion for the applicability of the Chabauty method to find the points of the curve Ch. We provide a framework which includes as a special case that used in Elliptic Curve Chabauty techniques and their higher genus versions. The set Ch(K) can be infinite only when C has genus at most 1; we analyze completely the case when C has genus 1.
Symplectic ID
516784
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Publication type
Journal Article
Publication date
01 Feb 2015