How can I define the degree of Frobenius map and its dual of abelian variety ?
In algebraic curve case, we define degree of frobenius by corresponding field extension(For example, see Silverman's Prop. 2.11).
But in general abelian variety case, how can I define degree of isogeny except for $[n]$ map ? (Degree of $[n]$ map is defined as order of its kernel)
Once degree of frobenius is defined, can we define dual isogeny $ \hat{Fr_p}$ by $[deg(Fr_p)]=Fr_p・\hat{Fr_p}$ in the same way as elliptic curve case?