unramified
- A morphism \(f: B\to A\) of rings is unramified iff it is finite type and the sheaf of relative differentials \(\Omega_{A/B}\)vanishes.
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A morphism \(f:X\to Y\) of schemes is unramified iff there exist affine opens \(U \subseteq X, f(U) \subseteq V\subseteq f(X)\) where the induced ring morphism \(U = \operatorname{Spec}B \to V=\operatorname{Spec}A\) is unramified.
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Equivalently, \(f\) is unramified iff \(f\) is locally of finite type and \(\Omega_{A/B}\) vanishes.
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Equivalently, \(f\) is unramified iff \(f\) is locally of finite type and \(\Omega_{A/B}\) vanishes.
Relation to ramification in number fields: 
