locally ringed space
English edit
Noun edit
locally ringed space (plural locally ringed spaces)
- (sheaf theory, scheme theory) An abstract mathematical object generalizing the relationship between spaces of functions and the germs of those functions at particular points (i.e. a ringed space) where the analogy with the motivating case is particularly strong. Formally, a topological space equipped with a sheaf of local rings (called the structure sheaf).
- Hypernym: ringed space Hyponym: scheme
Usage notes edit
Properly, a locally ringed space is a pair where is the space and is the structure sheaf. By abuse of notation, alone may also be referred to as a locally ringed space when is understood to be present in some context.