Timeline for Awfully sophisticated proof for simple facts
Current License: CC BY-SA 2.5
5 events
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| Oct 19, 2010 at 3:08 | comment | added | Chandan Singh Dalawat | My favourite proof of Kronecker-Weber is the one first given by Shafarevich and reproduced by Cassels in his Local Fields. You do the local case first (as in Lecture 19 of my notes arxiv.org/abs/0903.2615) and then nothing more than the Minkowski bound on the discriminant is needed to derive the theorem over $\mathbf Q$. | |
| Oct 18, 2010 at 20:12 | comment | added | Franz Lemmermeyer | If you google for "Kronecker-Weber via Stickelberger", you'll find a modern version of Weber's classical idea combined with Hilbert's idea of twisting. Washington's proof, if I remember correctly, derives the global version from the local one. There's even a proof in the Monthly: Am. Math. Mon. 81, 601-607 (1974), and a practically unknown proof based on Eisenstein reciprocity due to Delaunay (Delone). | |
| Oct 18, 2010 at 19:22 | comment | added | Kevin Buzzard | @Pete: I learnt number fields from a book by Marcus, and a proof is in there. IIRC there's also a proof very early on in Washington. | |
| Oct 18, 2010 at 15:52 | comment | added | Pete L. Clark | @Franz: I'll bet you know how to prove Kronecker-Weber without deducing it from a larger edifice of class field theory over $\mathbb{Q}$, but I'm sorry to tell you that most contemporary algebraic number theorists (including me) do not. | |
| Oct 18, 2010 at 15:45 | history | answered | Franz Lemmermeyer | CC BY-SA 2.5 |