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Computing p-adic heights on hyperelliptic curves

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  • UserStevan Gajović (Charles University)
  • ClockTuesday 14 November 2023, 14:30-15:30
  • HouseMR13.

If you have a question about this talk, please contact Jef Laga .

In this talk, we present an algorithm to compute p-adic heights on hyperelliptic curves with good reduction. Our algorithm improves a previous algorithm of Balakrishnan and Besser by being considerably simpler and faster and allowing even degree models. We discuss two applications of our work: to apply the quadratic Chabauty method for rational and integral points on hyperelliptic curves and to test the p-adic Birch and Swinnerton-Dyer conjecture in examples numerically. This is joint work with Steffen Müller.

This talk is part of the Number Theory Seminar series.

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DAMTP, room MR14 Cambridge University Engineering Department, LT6 Department of Materials Science, 27 Charles Babbage Road, Cambridge CB3 0FS

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