Group scheme | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-03-28

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Group_scheme


00:01:20 1 Definition
00:03:46 2 Constructions
00:07:34 3 Examples
00:12:00 4 Basic properties
00:14:58 5 Finite flat group schemes
00:17:58 6 Cartier duality
00:18:21 7 Dieudonné modules
00:21:02 8 See also



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:
https://assistant.google.com/services/invoke/uid/0000001a130b3f91
Other Wikipedia audio articles at:
https://www.youtube.com/results?search_query=wikipedia+tts
Upload your own Wikipedia articles through:
https://github.com/nodef/wikipedia-tts
Speaking Rate: 0.7832770425012192
Voice name: en-US-Wavenet-A


"I cannot teach anybody anything, I can only make them think."
- Socrates


SUMMARY
=======
In mathematics, a group scheme is a type of algebro-geometric object equipped with a composition law.  Group schemes arise naturally as symmetries of schemes, and they generalize algebraic groups, in the sense that all algebraic groups have group scheme structure, but group schemes are not necessarily connected, smooth, or defined over a field.  This extra generality allows one to study richer infinitesimal structures, and this can help one to understand and answer questions of arithmetic significance.  The category of group schemes is somewhat better behaved than that of group varieties, since all homomorphisms have kernels, and there is a well-behaved deformation theory.  Group schemes that are not algebraic groups play a significant role in arithmetic geometry and algebraic topology, since they come up in contexts of Galois representations and moduli problems.  The initial development of the theory of group schemes was due to Alexander Grothendieck, Michel Raynaud and Michel Demazure in the early 1960s.