Computing đť‘ť-adic heights on hyperelliptic curves
Stevan Gajović,
J. MĂĽller
Abstract:We describe an algorithm to compute the local Coleman–Gross
p
p
-adic height at
p
p
on a hyperelliptic curve. Previously, this was only possible using an algorithm due to Balakrishnan and Besser, which was limited to odd degree. While we follow their general strategy, our algorithm is significantly faster and simpler and works for both odd and even degree. We discuss a precision analysis and an implementation in SageMath. Our work has several applications, also discussed in t… Show more
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