Isogeny orbits in a family of abelian varieties

• Autorzy: Qian Lin , Ming-Xi Wang
• Języki publikacji: EN

Abstrakty

EN

We prove that if a curve of a nonisotrivial family of abelian varieties over a curve contains infinitely many isogeny orbits of a finitely generated subgroup of a simple abelian variety, then it is either torsion or contained in a fiber. This result fits into the context of the Zilber-Pink conjecture. Moreover, by using the polyhedral reduction theory we give a new proof of a result of Bertrand.

Kategorie tematyczne

• 11G50: Heights
• 14K12: Subvarieties
• 11G18: Arithmetic aspects of modular and Shimura varieties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 170
• Numer: 2
• Strony: 161-173

Daty

wydano

2015

Twórcy

autor

Qian Lin

• Center of Mathematical Sciences and Applications, Harvard University, Cambridge, MA 02138 U.S.A.

autor

Ming-Xi Wang

• Department of Mathematics, University of Salzburg, Hellbrunnerstr. 34/I, 5020 Salzburg, Austria

Identyfikatory

DOI

10.4064/aa170-2-4