### Reverse engineered hyperelliptic curves

Linfoot Number Theory Seminar

22nd March 2023, 11:00 am – 12:00 pm

Fry Building, Room 2.04

Falting's Theorem states that for any curve of genus >1, the set of rational points is finite. A lot of research effort is devoted to determining exactly the set of rational points that lie on a curve. In this talk, we're going in the opposite direction. We will show that for any finite set of rational points S, we can construct a hyperelliptic curve C/Q such that C(Q)=S.

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