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An ordinary abelian variety with an etale self-isogeny of p-power degree and no isotrivial factors
David Helm
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Semisimple pointed isogeny graphs for abelian varieties
Paul Alexander Helminck
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Isogeny formulas for Jacobi intersection and twisted hessian curves
João Paulo da Silva +2 more
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Cryptography is an essential tool for enabling privacy of electronic communication. However, many of the cryptographic protocols we use nowadays, would be insecure after the development of large-scale quantum computers. Therefore, the cryptographic community is preparing new protocols to replace the would-be broken ones. Protocols based on lattices are
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Horizontal isogeny theorems [PDF]
Summary: Let \(K\) be a field which is finitely generated over its prime field. Consider elliptic curves \(E\) and \(E'\) defined over \(K\). Suppose there exists \(c\geq 1\) and a set \(\Lambda\) of prime numbers such that \([K(E_l,E_l'): K(E_l)\cap K(E_l')]\leq c\) for all \(l\in\Lambda\).
Gerhard Frey, Moshe Jarden
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