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
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.
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author = {Jacob Tsimerman},
title = {The existence of an abelian variety over $\overline{\mathbb{Q}}$ isogenous to no {Jacobian}},
journal = {Annals of mathematics},
pages = {637--650},
year = {2012},
volume = {176},
number = {1},
doi = {10.4007/annals.2012.176.1.12},
mrnumber = {2925392},
zbl = {1250.14032},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2012.176.1.12/}
}
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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
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