Large degree primitive points on curves

Abstract

A number field $K$ is called primitive if $\mathbb{Q}$ and $K$ are the only subfields of $K$. Let $X$ be a nice curve over $\mathbb{Q}$ of genus $g$. A point $P$ of degree $d$ on $X$ is called primitive if the field of definition $\mathbb{Q}(P)$ of the point is primitive. In this short note we prove that if $X$ has a divisor of degree $d>2g$, then $X$ has infinitely many primitive points of degree $d$. This complements the results of Khawaja and Siksek that show that points of low degree are not primitive under certain conditions.

arXiv comment6 pages, Extended main result and corrected minor mistakes

Cited by in corpus (1)

• A single source theorem for primitive points on curves