Geodesic
Isogeny orbits in a family of abelian varieties
Qian Lin1 ; Ming-Xi Wang2
1 Center of Mathematical Sciences and Applications Harvard University Cambridge, MA 02138 U.S.A.
2 Department of Mathematics University of Salzburg Hellbrunnerstr. 34/I 5020 Salzburg, Austria
Acta Arithmetica, Tome 170 (2015) no. 2, pp. 161-173

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/aa170-2-4
Keywords: prove curve nonisotrivial family abelian varieties curve contains infinitely many isogeny orbits finitely generated subgroup simple abelian variety either torsion contained fiber result fits context zilber pink conjecture moreover using polyhedral reduction theory proof result bertrand

Qian Lin 1 ; Ming-Xi Wang 2

1 Center of Mathematical Sciences and Applications Harvard University Cambridge, MA 02138 U.S.A.
2 Department of Mathematics University of Salzburg Hellbrunnerstr. 34/I 5020 Salzburg, Austria 
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Qian Lin; Ming-Xi Wang. Isogeny orbits in a family of abelian varieties. Acta Arithmetica, Tome 170 (2015) no. 2, pp. 161-173. doi: 10.4064/aa170-2-4

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