For questions on ringed spaces or locally ringed spaces

A ringed space is a topological space together with a sheaf of commutative rings. Of particular interest are locally ringed spaces, which are ringed spaces in which each stalk of the sheaf of rings is a local ring. Morphisms of locally ringed spaces are also required to satisfy a locality condition.

Locally ringed spaces provide a general setting for "geometry". Important examples include schemes, complex analytic spaces, and smooth manifolds.