André–Pink conjecture for principally polarized abelian varieties

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Let Ag\mathcal{A}_g be the moduli space of principally polarized abelian varieties of dimension gg over C\mathbb{C}, let Z⊂AgZ\subset\mathcal{A}_g be an irreducible algebraic subvariety, and let Σ\Sigma be a polarized isogeny class in Ag\mathcal{A}_g. André–Pink conjecture. If Σ∩Z\Sigma\cap Z is Zariski dense in ZZ, then ZZ is a special subvariety of Ag\mathcal{A}_g. This is an André–Pink-type unlikely-intersection statement relating polarized isogeny classes to special subvarieties; the supplied text gives no resolution status.

References

Primary source

Martin Orr, “On compatibility between isogenies and polarisations of abelian varieties”, arXiv:1506.04011 (2016).

Additional references

2 papers in this index state this conjecture (2012–2015). The statement above is taken from the most recent of them; the others are arXiv:1209.3653.

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