I want to know more classes of examples of locally ringed spaces. The reason is that when I want to prove/disprove something about locally ringed spaces, my examples are often not eclectic enough. Besides, it is interesting to what extent special theories can be generalized to locally ringed spaces.
Here are the classes of examples I know:
- Local rings (underlying topological space is a point)
- Algebraic Varieties in the classical sense (just closed points)
- Manifolds with smooth/analytic/holomorphic functions
- Topological spaces with continuous functions
- Various subcategories of the above examples
- The category of locally ringed spaces is complete and cocomplete. Thus you can build new locally ringed spaces out of the above ones.
Which substantial different examples do you know? Please no fancy Grothendieck topologies ;).