Cyclic Isogenies for Abelian Varieties with Real Multiplication
ROBERT, Damien
Lithe and fast algorithmic number theory [LFANT]
Laboratoire International de Recherche en Informatique et Mathématiques Appliquées [LIRIMA]
Université de Bordeaux [UB]
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Lithe and fast algorithmic number theory [LFANT]
Laboratoire International de Recherche en Informatique et Mathématiques Appliquées [LIRIMA]
Université de Bordeaux [UB]
ROBERT, Damien
Lithe and fast algorithmic number theory [LFANT]
Laboratoire International de Recherche en Informatique et Mathématiques Appliquées [LIRIMA]
Université de Bordeaux [UB]
< Leer menos
Lithe and fast algorithmic number theory [LFANT]
Laboratoire International de Recherche en Informatique et Mathématiques Appliquées [LIRIMA]
Université de Bordeaux [UB]
Idioma
en
Article de revue
Este ítem está publicado en
Moscow Mathematical Journal. 2022, vol. 22, n° 4, p. 613-655
Independent University of Moscow
Resumen en inglés
We study quotients of principally polarized abelian varieties with real multiplication by Galois-stable finite subgroups and describe when these quotients are principally polarizable. We use this characterization to provide ...Leer más >
We study quotients of principally polarized abelian varieties with real multiplication by Galois-stable finite subgroups and describe when these quotients are principally polarizable. We use this characterization to provide an algorithm to compute explicit cyclic isogenies from kernel for abelian varieties with real multiplication over finite fields. Our algorithm is polynomial in the size of the finite field as well as in the degree of the isogeny and is based on Mumford's theory of theta functions and theta embeddings. Recently, the algorithm has been successfully applied to obtain new results on the discrete logarithm problem in genus 2 as well as to study the discrete logarithm problem in genus 3.< Leer menos
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