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Debarre–Pareschi–Popa conjecture on minimal cohomology classes in principally polarized abelian varieties
Debarre–Pareschi–Popa conjecture. The following are equivalent: (1) $X$ is reduced, of pure dimension, and has minimal cohomology class
Conjectureopenabelian-varieties generic-vanishing minimal-cohomology-classesarXiv posted 2 days ago

Debarre–Pareschi–Popa conjecture on minimal cohomology classes in principally polarized abelian varieties