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See http://www.math.nyu.edu/~tschinke/books/finite-fields/final/05_oort.pdf, Section 15:
If I understand this correctly, onlyOnly Type III and IV can occur, and III only for dimension $1$ or $2$.
If I understand this correctly, only Type III and IV can occur.
Only Type III and IV can occur, and III only for dimension $1$ or $2$.
