Finite Weil restriction of curves

Abstract

Given number fields $L\supset K$, smooth projective curves $C$ defined over $L$ and $B$ defined over $K$, and a non-constant $L$-morphism $h:C\to B_L$,we consider the curve $C_h$ defined over $K$ whose $K$-rational points parametrize the $L$-rational points on $C$ whose images under $h$ are defined over $K$. Our construction provides a framework which includes as a special case that used in Elliptic Curve Chabauty techniques and their higher genus versions. The set $C_h(K)$ can be infinite only when $C$ has genus at most 1; we analyze completely the case when $C$ has genus 1.

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References in corpus (1)

• Explicit Chabauty over Number Fields

Cited by in corpus (1)

• Elliptic Curves over Real Quadratic Fields are Modular