Ringed space | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-03-28

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Ringed_space


00:00:54 1 Definitions
00:01:26 2 Examples
00:02:35 3 Morphisms
00:03:51 4 Tangent spaces
00:05:04 5 iOsubX/sub/i modules



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SUMMARY
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In mathematics, a ringed space is a family of (commutative) rings parametrized by open subsets of a topological space together with ring homomorphisms that play roles of restrictions. Precisely, it is 
a topological space equipped with a sheaf of rings called a structure sheaf. It is an abstraction of the concept of the rings of continuous (scalar-valued) functions on open subsets.
Among ringed spaces, especially important and prominent is a locally ringed space: a ringed space in which the analogy of a germ of a function is valid.
Ringed spaces appear in analysis as well as complex algebraic geometry and scheme theory of algebraic geometry.
Note: In the definition of a ringed space, most expositions tend to restrict the rings to be commutative rings, including Hartshorne and Wikipedia. "Éléments de géométrie algébrique", on the other hand, does not impose the commutativity assumption, although the book mostly considers the commutative case.