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

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

2010-10-11

arxiv.org/abs/1010.2181v1

Mathematics

Number Theory

Scientific paper

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 Andr\'e-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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