Around the support problem for Hilbert class polynomials

  • Francesco Campagna

    Université Clermont Auvergne, Aubière, France
  • Gabriel A. Dill

    Université de Neuchâtel, Switzerland
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Abstract

Let denote the Hilbert class polynomial of the imaginary quadratic order of discriminant . We study the rate of growth of the greatest common divisor of and as for and belonging to various Dedekind domains. We also study the modular support problem: if for all but finitely many every prime ideal dividing also divides , what can we say about and ? If we replace by and the Dedekind domain is a ring of -integers in some number field, then these are classical questions that have been investigated by Bugeaud–Corvaja–Zannier, Corvaja–Zannier, and Corrales-Rodrigáñez–Schoof.

Cite this article

Francesco Campagna, Gabriel A. Dill, Around the support problem for Hilbert class polynomials. Comment. Math. Helv. 100 (2025), no. 3, pp. 421–462

DOI 10.4171/CMH/596