Timeline for Expository articles on Algebraic Number Theory
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 26, 2016 at 8:46 | vote | accept | rationalbeing | ||
| May 26, 2016 at 12:29 | |||||
| May 21, 2016 at 3:02 | comment | added | KConrad | Not only is the first title long, but it's awkward in English. (I can't judge how the analogue of it in your native language would sound, or maybe you are going to write it in English.) The second one definitely sounds better. | |
| May 21, 2016 at 2:59 | comment | added | rationalbeing | @KConrad see the problem is that, as a small project, I am going to study algebraic number theory before class field theory but I don't find it pleasing to call my report "Some topic in Algebraic Number Theory" since it's really long title. Any suggestions? Do you think "Number Fields" would make a better title? Sorry for unnecessary botheration. | |
| May 20, 2016 at 20:04 | comment | added | KConrad | @rationalbeing, just google all the books on algebraic number theory you can find and look at the table of contents before they reach class field theory (many don't even get to that point). You'll see what is covered. I would just call it algebraic number theory. It doesn't have another standard name. Highlights include unique factorization of ideals, the ideal class group, the unit theorem, ramification (discriminant/different), features of Galois extensions (decomposition/inertia groups, Frobenius elements), and some examples (e.g., quadratic and cyclotomic fields) and applications. | |
| May 20, 2016 at 18:59 | comment | added | Samantha Y | my own undereducated guess might be that it's more like 'algebraic number theory' as the body of literature/techniques/problems, with class field theory at/as its heart (see also the first book of the number theory trilogy by Kato et al., books.google.com/…) | |
| May 20, 2016 at 17:54 | comment | added | rationalbeing | @KConrad what would you call the part of Algebraic number theory before class field theory? Just curious to know the two main parts in which one would divide whole of Algebraic number theory. | |
| May 20, 2016 at 15:25 | comment | added | KConrad | @rationalbeing, a one-semester course already has so much material to cover that it is usually not feasible to reach class field theory except maybe to say briefly something about the main theorems; certainly there's no time to "get into" class field theory in depth. If you take an algebraic number theory course, or later try to teach such a course, you'll understand why. Your question is sort of like asking why a first calculus course doesn't get to Stokes' theorem. | |
| May 20, 2016 at 15:21 | comment | added | rationalbeing | Yes, it's nice article. I have a curiosity : "Why do most 1 semester courses on Algebraic number theory end before getting into class field theory?". Can you satisfy this curiosity? | |
| May 20, 2016 at 15:02 | history | answered | Samantha Y | CC BY-SA 3.0 |