Differential criterion for separability of an isogeny
= Differential criterion for separability of an isogeny
{title2=$\phi^*\omega\ne0$}
A nonzero <isogeny of elliptic curves> is separable exactly when its pullback of an <invariant differential on an elliptic curve> is nonzero. For a map of smooth curves in characteristic $p$, a zero differential means the function-field extension has a nontrivial inseparable part. The criterion turns sums of elliptic endomorphisms into computations of their tangent scalars.