= Finite étale morphism
A finite étale morphism is both a <finite morphism> and an <étale morphism>. Affine-locally it is represented by a finite locally free algebra with zero module of <Kähler differentials>. Its fibres are finite products of finite separable field extensions. For an <elliptic curve> with <good reduction> at a prime not dividing $m$, multiplication by $m$ on its smooth proper group model is finite étale of degree $m^2$: its differential is multiplication by the unit $m$. A division torsor of a section consequently gives an unramified local extension, the good-prime input to the <Weak Mordell-Weil theorem>.
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