A locally ringed space is a common generalization of schemes and various manifolds. I am wondering about a locally ringed group which should be a common generalization of group schemes and various Lie groups.

Questions: did anyone ever work it out? are there any references?

Comment: when I try to reinvent it my wings take dream very soon: the multiplication is defined $G\times G \rightarrow G$ but $G\times G$ should not be a product of topological spaces, it is not for the schemes...