Finite Weil Restriction of Curves

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.