Sheaf of Kähler differentials over a field
= Sheaf of Kähler differentials over a field
{title2=$\Omega^1_{X/k}$}
= Kähler differential sheaf
{c}
{synonym}
For a <variety> over $k$, the <Module of Kähler differentials> $\Omega_{A/k}$ on each <affine chart> gives a <quasi-coherent sheaf>. Compatibility with <localization> glues these into $\Omega^1_{X/k}$. A <finite presentation of an algebra> gives a <finite presentation of a module> for its differentials, so this is a <coherent sheaf> on a <variety>.