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We prove (by a case-by-case analysis) a conjecture of Bernstein/Schwarzman tothe effect that quotients of abelian varieties by suitable actions of (complex)reflection groups are weighted projective spaces, and show that this remainstrue after reduction to finite characteristic (including characteristicsdividing the order of the group!). We also show that an analogous statementholds (with five explicitly enumerated exceptions) for actions of quaternionicreflection groups on supersingular abelian varieties.

Quotients of abelian varieties by reflection groups