Let $X$ be an abelian variety over a finite field of characteristic $p$ such that the $X[p]=0$. In other words, none of the Newton slopes are $0,1$. 


**QUESTIONS.**


(a) Is it possible for the endomorphism algebra $End(X)$ to be commutative? 


(b) If so, are there examples that are fairly easy to construct?



Abelian varieties with p-rank zero
(a) Oh, yes. This is proven in a paper of Hendrik Lenstra and Frans Oort 
<http://www.sciencedirect.com/science/article/pii/0022404974900292> .


(b) A construction of the corresponding CM-field of endomorphisms is described in the paper mentioned above.


