 Canonical line bundle of a smooth variety

For a smooth $n$-dimensional variety $X$ over a field, its canonical line bundle is ${\omega }_X={\bigwedge }^n{\Omega }_{X/k}^1$. It is the bundle of top-degree algebraic differential forms. A nonzero rational section defines a canonical divisor of a smooth variety. This algebraic definition works in arbitrary characteristic and is distinct from restricting the analytic canonical-bundle definition to complex manifolds.