JEDNOSTKA NAUKOWA KATEGORII A+

Algebraic relations over finite fields that preserve the endomorphism rings of CM $j$-invariants

Francesco Campagna, Gabriel A. Dill Acta Arithmetica MSC: Primary 11G15; Secondary 11G18 DOI: 10.4064/aa240123-12-11 Opublikowany online: 13 March 2025

Streszczenie

We characterise the integral affine plane curves over a finite field $k$ with the property that all but finitely many of their $\overline {k}$-points have coordinates that are $j$-invariants of elliptic curves with isomorphic endomorphism rings. This settles a finite field variant of the André–Oort conjecture for $Y(1)^2_\mathbb {C}$, which is a theorem of André. We use our result to solve the modular support problem for function fields of positive characteristic.

Autorzy

  • Francesco CampagnaUniversité Clermont Auvergne – LMBP
    UMR 6620 – CNRS
    Campus des Cézeaux
    3, Place Vasarely
    63178 Aubière Cedex, France
    e-mail
  • Gabriel A. DillInstitut de Mathématiques
    Université de Neuchâtel
    Rue Emile-Argand 11
    2000 Neuchâtel, Switzerland
    e-mail

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek