locally ringed space
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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.