Geodesic
Isogeny orbits in a family of abelian varieties
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
Acta Arithmetica, Tome 170 (2015) no. 2, pp. 161-173 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

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 
@article{10_4064_aa170_2_4,
     author = {Qian Lin and Ming-Xi Wang},
     title = {Isogeny orbits in a family of abelian varieties},
     journal = {Acta Arithmetica},
     pages = {161--173},
     year = {2015},
     volume = {170},
     number = {2},
     doi = {10.4064/aa170-2-4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/aa170-2-4/}
}
TY  - JOUR
AU  - Qian Lin
AU  - Ming-Xi Wang
TI  - Isogeny orbits in a family of abelian varieties
JO  - Acta Arithmetica
PY  - 2015
SP  - 161
EP  - 173
VL  - 170
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4064/aa170-2-4/
DO  - 10.4064/aa170-2-4
LA  - en
ID  - 10_4064_aa170_2_4
ER  - 
%0 Journal Article
%A Qian Lin
%A Ming-Xi Wang
%T Isogeny orbits in a family of abelian varieties
%J Acta Arithmetica
%D 2015
%P 161-173
%V 170
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4064/aa170-2-4/
%R 10.4064/aa170-2-4
%G en
%F 10_4064_aa170_2_4
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

Cité par Sources :