André–Pink conjecture with unpolarized isogeny classes

Let Ag\mathcal{A}_g be the moduli space of principally polarized abelian varieties of dimension gg over C\mathbb{C}, and let ZAgZ\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.

Sources & referencesView supporting material

Primary source

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

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