Hilbert modular polynomials

Chloe Martindale*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)

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 varieties with maximal real multiplication by a fixed totally real number field . In the 2-dimensional case with we also provide an implementation together with some optimisations specific to this case. We also explain applications of this algorithm to point counting, walking on isogeny graphs, and computing class polynomials.
Original languageEnglish
Pages (from-to)464-498
Number of pages35
JournalJournal of Number Theory
Volume213
Early online date18 Mar 2020
DOIs
Publication statusPublished - 1 Aug 2020

Keywords

  • Abelian varieties
  • Cyclic isogenies
  • Genus two
  • Hilbert modular polynomials
  • Maximal real multiplication

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