Frobenius Finds Non-monogenic Division Fields of Abelian Varieties

Hanson Smith

Let $A$ be an abelian variety over a finite field $k$ with $|k|=q=p^m$. Let $\pi \in {\text{End}}_k(A)$ denote the Frobenius and let $v=\frac{q}{\pi }$ denote Verschiebung. Suppose the Weil…