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

Linfoot Number Theory Seminar

11th November 2020, 11:00 am – 12:00 pm

Virtual Seminar, https://zoom.us/j/97981256193

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.

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