= Sheaf of units of the structure sheaf
{title2=$\mathcal O_X^*$}
The units in the <structure sheaf of a scheme> form a multiplicative <sheaf of abelian groups>. On a <smooth algebraic curve>, a nonzero <rational function> is a unit at a point precisely when its <discrete valuation> there is zero. Its inclusion in the <sheaf of nonzero rational functions on an irreducible variety> relates <divisor on an algebraic curve> to the <Picard group> through the <long exact sequence in sheaf cohomology>.
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