Counting fields generated by points on plane curves

Abstract: For a smooth projective curve $C/\mathbb{Q}$, how many field extensions of $\mathbb{Q}$ -- of given degree and bounded discriminant --- arise from adjoining a point of $C(\overline{\mathbb{Q}})$? Can we further count the number of such extensions with a specified Galois group? Asymptotic lower bounds for these quantities have been found for elliptic curves by Lemke Oliver and Thorne, for hyperelliptic curves by Keyes, and for superelliptic curves by Beneish and Keyes. We discuss similar asymptotic lower bounds that hold for all smooth plane curves $C$.

number theory

Audience: researchers in the topic

Harvard number theory seminar