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arXiv · 1210.4407

Finite Weil restriction of curves

E. V. Flynn·D. Testa
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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 $h \colon C \to B_L$,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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E. V. Flynn, D. Testa. 2012-10-16. Finite Weil restriction of curves. https://arxiv.org/abs/1210.4407

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