# The existence of an abelian variety over $\overline{\mathbb{Q}}$ isogenous to no Jacobian | Annals of Mathematics

Abstract We prove the existence of an abelian variety A of dimension g over 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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### 数学年刊（Annals of Mathematics）

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