Rational section of a line bundle
= Rational section of a line bundle
On an <integral scheme> with <generic point> $\eta$ and function field $K$, a rational section of a <line bundle> $\mathcal L$ is an element of the one-dimensional $K$-space $\mathcal L_\eta$. A nonzero rational section writes as $a_ie_i$ in local trivializations, with $a_i\in K^*$. Ratios of these coefficients are regular units, and therefore define a <Cartier divisor>.