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Let Ag be the moduli space over Fₚ of g-dimensional principally polarised abelian varieties, where p is a prime. We show that if g is even and p 5, then every geometric generic member in the maximal supersingular Ekedahl-Oort stratum in Ag has automorphism group \ 1\. This confirms Oort's conjecture in the case of p 5 and even g.
Karemaker et al. (Fri,) studied this question.