Constant sheaves on irreducible spaces are flasque

Every nonempty open subset of an irreducible space is connected. A locally constant function into a fixed abelian group $D$ is therefore constant on that open set. Restrictions between nonempty opens identify with the identity of $D$, and restrictions to the empty set are surjective onto zero. Thus the constant sheaf is flasque, with global sections $D$ and zero higher sheaf cohomology on a nonempty irreducible space. For an integral scheme its constant function-field sheaf has its natural structure-sheaf action by regular functions viewed in the function field.