Computing rational points on databases of curves

Abstract: For a curve of genus at least $2$, we know from Faltings's theorem that its set of rational points is finite. A major challenge is to provably determine, for a given curve, this set of rational points. One promising method is the Chabauty-Coleman method, which uses $p$-adic (Coleman) integrals to compute a finite set of p-adic points on the curve including the rational points. We will discuss computations using the Chabauty-Coleman method to provably determine rational point sets for databases of certain genus $3$ superelliptic curves. This is joint work with Maria de Frutos Fernandez and Travis Morrison.

number theory

Audience: researchers in the discipline

Comments: Please register for the talks on August 10 here: fordham.zoom.us/meeting/register/tJwpde2srTgqHdYG6NMu5WmgzPiDnNJQMTsM

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POINT: New Developments in Number Theory

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