Add to ORKGWe 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
Abstract. An isogeny graph is a graph whose vertices are principally polarized abelian varieties and...
We describe an efficient algorithm for the computation of isogenies between abelian varieties repres...
We describe an efficient algorithm for the computation of isogenies between abelian varieties repres...
We study quotients of principally polarized abelian varieties with real multiplication by Galois-sta...
We study quotients of principally polarized abelian varieties with real multiplication by Galois-sta...
Abelian varieties are fascinating objects, combining the fields of geometry and arithmetic. While th...
Fix a prime number l. Graphs of isogenies of degree a power of l are well-understood for elliptic cu...
In this thesis we address the problem of developing effective algorithms to compute isomorphism clas...
In this thesis we address the problem of developing effective algorithms to compute isomorphism clas...
In this thesis we address the problem of developing effective algorithms to compute isomorphism clas...
We give algorithms to compute isomorphism classes of ordinary abelian varieties defined over a finit...
We give algorithms to compute isomorphism classes of ordinary abelian varieties defined over a finit...
We give algorithms to compute isomorphism classes of ordinary abelian varieties defined over a finit...
Abstract. An isogeny graph is a graph whose vertices are principally polarized abelian varieties and...
We give algorithms to compute isomorphism classes of ordinary abelian varieties defined over a finit...
Abstract. An isogeny graph is a graph whose vertices are principally polarized abelian varieties and...
We describe an efficient algorithm for the computation of isogenies between abelian varieties repres...
We describe an efficient algorithm for the computation of isogenies between abelian varieties repres...
We study quotients of principally polarized abelian varieties with real multiplication by Galois-sta...
We study quotients of principally polarized abelian varieties with real multiplication by Galois-sta...
Abelian varieties are fascinating objects, combining the fields of geometry and arithmetic. While th...
Fix a prime number l. Graphs of isogenies of degree a power of l are well-understood for elliptic cu...
In this thesis we address the problem of developing effective algorithms to compute isomorphism clas...
In this thesis we address the problem of developing effective algorithms to compute isomorphism clas...
In this thesis we address the problem of developing effective algorithms to compute isomorphism clas...
We give algorithms to compute isomorphism classes of ordinary abelian varieties defined over a finit...
We give algorithms to compute isomorphism classes of ordinary abelian varieties defined over a finit...
We give algorithms to compute isomorphism classes of ordinary abelian varieties defined over a finit...
Abstract. An isogeny graph is a graph whose vertices are principally polarized abelian varieties and...
We give algorithms to compute isomorphism classes of ordinary abelian varieties defined over a finit...
Abstract. An isogeny graph is a graph whose vertices are principally polarized abelian varieties and...
We describe an efficient algorithm for the computation of isogenies between abelian varieties repres...
We describe an efficient algorithm for the computation of isogenies between abelian varieties repres...