Geodesic
The existence of an abelian variety over $\overline{\mathbb{Q}}$ isogenous to no Jacobian
Jacob Tsimerman1
1 Department of Mathematics, Harvard University, One Oxford Street, Cambridge, MA 02138
Annals of mathematics, Tome 176 (2012) no. 1, pp. 637-650.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We prove the existence of an abelian variety $A$ of dimension $g$ over $\overline{\mathbb{Q}}$ that is not isogenous to any Jacobian, subject to the necessary condition $g\!>\!3$. Recently, C. Chai and F. Oort gave such a proof assuming the André-Oort conjecture. We modify their proof by constructing a special sequence of CM points for which we can avoid any unproven hypotheses. We make use of various techniques from the recent work of Klingler-Yafaev et al.
DOI : 10.4007/annals.2012.176.1.12

Jacob Tsimerman 1

1 Department of Mathematics, Harvard University, One Oxford Street, Cambridge, MA 02138 
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Jacob Tsimerman. The existence of an abelian variety over $\overline{\mathbb{Q}}$ isogenous to no Jacobian. Annals of mathematics, Tome 176 (2012) no. 1, pp. 637-650. doi : 10.4007/annals.2012.176.1.12. http://geodesic.mathdoc.fr/articles/10.4007/annals.2012.176.1.12/

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