Algebraic space | Wikipedia audio article

This is an audio version of the Wikipedia Article:


00:01:04 1 Definition
00:01:30 1.1 Algebraic spaces as quotients of schemes
00:05:41 1.2 Algebraic spaces as sheaves
00:08:03 2 Algebraic spaces and schemes
00:11:02 3 Algebraic spaces and analytic spaces
00:12:25 4 Generalization



Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.

Learning by listening is a great way to:
- increases imagination and understanding
- improves your listening skills
- improves your own spoken accent
- learn while on the move
- reduce eye strain

Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone.

Listen on Google Assistant through Extra Audio:
Other Wikipedia audio articles at:
Upload your own Wikipedia articles through:
Speaking Rate: 0.8274402503424305
Voice name: en-AU-Wavenet-C


"I cannot teach anybody anything, I can only make them think."
- Socrates


SUMMARY
=======
In mathematics, algebraic spaces form a generalization of the schemes of algebraic geometry, introduced by Artin (1969, 1971) for use in deformation theory. Intuitively,
schemes are given by gluing together affine schemes using the Zariski topology, while algebraic spaces are given by gluing together affine schemes using the finer étale topology. Alternatively one can think of schemes as being locally isomorphic to affine schemes in the Zariski topology, while algebraic spaces are locally isomorphic to affine schemes in the étale topology.
The resulting category of algebraic spaces extends the category of schemes and allows one to carry out several natural constructions that are used in the construction of moduli spaces but are not always possible in the smaller category of schemes, such as taking the quotient of a free action by a finite group (cf. the Keel–Mori theorem).