Tangent sheaf of a scheme
= Tangent sheaf of a scheme
{title2=$\mathcal T_{X/S}=\mathcal H om(\Omega^1_{X/S},\mathcal O_X)$}
The relative tangent sheaf is the <dual of a sheaf> of <Kähler differentials>. Its sections are derivations of the <structure sheaf> that kill base scalars. For a <smooth morphism> it is <locally free> and describes first-order deformations of sections into the scheme.