Timeline for Neat applications of Galois descent?
Current License: CC BY-SA 3.0
8 events
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| Jan 22, 2017 at 13:23 | comment | added | nfdc23 | Ah, I didn't realize the last sentence of your first comment is intended as separate from the motivation aspect; sorry about that. (The process of convincing myself that a topic isn't empty abstraction is very much tied up with the process of acquiring enough motivation to learn it, so it hadn't occurred to me that the two can be considered separately.) The Serre and Gille-Szamuely books provide many examples that can be appreciated without extensive knowledge of algebraic geometry, essentially being about "affine" objects, so they should be quite apt for illustration purposes in your seminar. | |
| Jan 22, 2017 at 11:46 | comment | added | Arrow | @nfdc23 thank you very much for the recommendation. I feel you have unfairly twisted my words - I did not say I was motivated by the authors' names, only that they assured me categorical Galois theory isn't empty abstraction. Curiosity motivated me :) | |
| Jan 22, 2017 at 8:11 | comment | added | მამუკა ჯიბლაძე | @QiaochuYuan In a recent answer you also described a quite accessible example of how Galois descent can be used to obtain interesting information about Hopf algebras over non-algebraically-closed fields. | |
| Jan 22, 2017 at 3:13 | comment | added | nfdc23 | OK, though I recommend having more tangible prior motivation than "a famous person wrote about this" before deciding to dive into a topic. Anyway, section 1 of Chapter III of Serre's classic book Galois cohomology (building on the general formalism he sets up in section 5 of Chapter I) is the standard succinct reference on important basic examples of Galois descent. The more recent book Central Simple Algebras and Galois Cohomology by Gille and Szamuely contains a wealth of significant examples and applications worked out in extensive detail (see its table of contents). | |
| Jan 22, 2017 at 2:41 | comment | added | Qiaochu Yuan | I give some simple examples here: qchu.wordpress.com/2015/11/17/forms-and-galois-cohomology | |
| Jan 22, 2017 at 1:30 | comment | added | Arrow | I like categories and thought it's cool a single formalism encompasses different fields. I never felt I needed explicit classical Galois stuff for motivation. I only mean I'm comfortable with the categorical stuff in the sense I feel I understand the covering space aspect of the abstractions. The fact esteemed category theorists wrote a book on the topic was enough to make me feel it's not empty abstraction :) | |
| Jan 22, 2017 at 1:16 | comment | added | nfdc23 | Out of curiosity, why did you teach yourself categorical Galois theory without first being aware of some of the interesting applications of traditional Galois descent? In what sense does one become comfortable with a theorem without knowing how to illustrate that it is not empty abstraction? | |
| Jan 22, 2017 at 0:58 | history | asked | Arrow | CC BY-SA 3.0 |