= Sheaf of nonzero rational functions on an irreducible variety
{title2=$\mathcal K_X^*$}
For an irreducible <algebraic variety> $X$ with <function field> $K$, this <sheaf of abelian groups> assigns $K^*$ to every nonempty open set, with identity restriction maps, and assigns the trivial group to the empty set. Irreducibility ensures that any two nonempty open subsets meet, so these sections satisfy the <sheaf gluing axiom>. It is a <flasque sheaf> and has zero higher <sheaf cohomology>.
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