= Canonical line bundle of a smooth variety
{title2=$\omega_X=\bigwedge^n\Omega^1_{X/k}$}
For a smooth $n$-dimensional variety $X$ over a field, its canonical <line bundle> is $\omega_X=\bigwedge^n\Omega^1_{X/k}$. 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.
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