This the definition from Hartshorne's Algebraic Geometry of Smooth of relative dimension n
I want to understand what is meant by $\Omega_{X/Y}\times k(x)$.
$\Omega_{X/Y}$ is the sheaf of relative differentials of X over Y which is a quasi-coherent sheaf of modules over $X$ and $k(x)=\frac{\mathcal O_{X,x}}{m_x}$ , which is a field. What is meant by tensoring
a sheaf with a field?