Antonela Trbović

Splitting of primes in number fields generated by points on some modular curves

We talk about the splitting of primes in number fields generated by points on some modular curves. Momose was the first to notice that quadratic points on X_1(n) generate quadratic fields over which certain primes split in a particular way and his results were later expanded upon by Krumm. We prove results about the splitting behaviour of primes in quadratic fields generated by points on the modular curves X_0(n) which are hyperelliptic (except for n=37) and in cubic fields generated by points on X_1(2,14). This is joint work with Filip Najman.