Maleeha Khawaja

Primitive algebraic points on curves

A number field K is primitive if K and Q are the only sub extensions of K. Let C be a curve over Q with genus g, with g greater than or equal to 2. An algebraic point P on C is primitive if the number field Q(P) is primitive.
For example, quadratic fields are the simplest example of primitive number fields. By a theorem of Hindry and Silverman, if C is neither hyperelliptic nor bielliptic then C has finitely many quadratic points.
Let d be an integer. We present some sufficient conditions for C to have finitely many primitive degree d points. On the contrary, we show that if d is big enough (with respect to g) then C has infinitely many primitive degree d points, given the existence of one such point. This is joint work with Samir Siksek.