André–Pink conjecture with unpolarized isogeny classes

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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}, and let Z⊂AgZ\subset\mathcal{A}_g be an irreducible algebraic subvariety. André–Pink conjecture with unpolarized isogeny classes. The André–Pink conjecture for Ag\mathcal{A}_g should remain true when “a polarized isogeny class Σ\Sigma” is replaced by “an isogeny class Σ\Sigma.” The text presents this as a priori slightly stronger and more natural from the perspective of abelian varieties, but supplies no resolution status.

References

Primary source

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

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