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Heights and isogenies of Drinfeld modules

Volume 197 / 2021

Florian Breuer, Fabien Pazuki, Mahefason Heriniaina Razafinjatovo Acta Arithmetica 197 (2021), 111-128 MSC: Primary 11G09; Secondary 11G50, 14G17, 14G40. DOI: 10.4064/aa191029-8-7 Published online: 5 October 2020

Abstract

We provide explicit bounds on the difference of heights of isogenous Drinfeld modules. We derive a finiteness result in isogeny classes. In the rank 2 case, we also obtain an explicit upper bound on the size of the coefficients of modular polynomials attached to Drinfeld modules.

Authors

  • Florian BreuerSchool of Mathematical
    and Physical Sciences
    University of Newcastle
    University Drive
    Callaghan 2308 NSW, Australia
    e-mail
  • Fabien PazukiInstitute of Mathematics
    University of Copenhagen
    Universitetsparken 5
    2100 København, Denmark
    and
    Institut de Mathématiques de Bordeaux
    Université de Bordeaux
    Cours de la Libération
    33400 Talence, France
    e-mail
  • Mahefason Heriniaina RazafinjatovoDépartement de Mathématiques
    et Informatique
    Université d’Antananarivo
    BP 906, Antananarivo 101, Madagascar
    e-mail

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