Hilbert Modular Polynomials
MARTINDALE, Chloe
Universiteit Leiden = Leiden University
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Universiteit Leiden = Leiden University
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
MARTINDALE, Chloe
Universiteit Leiden = Leiden University
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
< Reduce
Universiteit Leiden = Leiden University
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]
Language
en
Article de revue
This item was published in
Journal of Number Theory. 2020, vol. 213, p. 464-498
Elsevier
English Abstract
We present an algorithm to compute a higher dimensional analogue of modular polynomials. This higher dimensional analogue, the 'set of Hilbert modular polynomials', concerns cyclic isogenies of principally polarised abelian ...Read more >
We present an algorithm to compute a higher dimensional analogue of modular polynomials. This higher dimensional analogue, the 'set of Hilbert modular polynomials', concerns cyclic isogenies of principally polarised abelian varieties with maximal real multiplication by a fixed totally real number field K0. We give a proof that this algorithm is correct, and provide practical improvements and an implementation for the 2-dimensional case with K0 = Q(√ 5). We also explain applications of this algorithm to point counting, walking on isogeny graphs, and computing class polynomials.Read less <
English Keywords
Hilbert modular polynomials
Cyclic isogenies
Abelian varieties
Genus two
Maximal real multiplication
Origin
Hal imported