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arXiv · 1010.2181

The Existence of an Abelian Variety over the Algebraic Numbers isogenous to no Jacobian

Jacob Tsimerman
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Abstract

We prove the existence of an Abelian variety $A$ of dimension $g$ over $\Qa$ which 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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Jacob Tsimerman. 2010-10-11. The Existence of an Abelian Variety over the Algebraic Numbers isogenous to no Jacobian. https://arxiv.org/abs/1010.2181

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