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