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Computing isogenies between Jacobians of hyperelliptic curves of arbitrary genus via differential equations

Elie Eid 1, 2
2 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : Let $p$ be an odd prime number and be an integer coprime to $p$. We survey an algorithm for computing explicit rational representations of $(\ell,...,\ell)$-isogenies between Jacobians of hyperelliptic curves of arbitrary genus over an extension $K$ of the field of $p$-adic numbers $\mathbb{Q}_p$. The algorithm has a quasi-linear complexity in $\ell$ as well as in the genus of the curves.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03142205
Contributor : Elie Eid Connect in order to contact the contributor
Submitted on : Monday, February 15, 2021 - 7:38:59 PM
Last modification on : Friday, May 20, 2022 - 9:04:51 AM
Long-term archiving on: : Sunday, May 16, 2021 - 8:02:08 PM

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  • HAL Id : hal-03142205, version 1
  • ARXIV : 2102.08018

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Elie Eid. Computing isogenies between Jacobians of hyperelliptic curves of arbitrary genus via differential equations. 2021. ⟨hal-03142205⟩

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