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Cotangent sheaf

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In algebraic geometry, given a morphism f: X → S of schemes, the cotangent sheaf on X is the sheaf of O X {\displaystyle {\mathcal {O}}_{X}} -modules Ω X / S {\displaystyle \Omega _{X/S}} that represents (or classifies) S-derivations in the sense: for any O X {\displaystyle {\mathcal {O}}_{X}} -modules F, there is an isomorphism