Timeline for About principal ideal theorem in number fields
Current License: CC BY-SA 3.0
13 events
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Jul 18, 2019 at 2:04 | vote | accept | kjs | ||
Nov 11, 2013 at 12:59 | history | edited | Ricardo Andrade | CC BY-SA 3.0 |
added top level tag, minor reformatting
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Nov 11, 2013 at 11:28 | answer | added | Filippo Alberto Edoardo | timeline score: 3 | |
Nov 11, 2013 at 2:44 | comment | added | kjs | @FranzLemmermeyer: Thank you for your comment. I was originally interested in the case Gal($K$/$Q$) = (p) where p is odd prime and didn't consider the cases in the paper you mentioned. I'm a little bit confused about the definition, though. From your survey paper "class field towers(2010)", it seems (2,4)-extension means a field $K$ with Gal($K$/$Q$) = (2,4). Am I right? If so, can you suggest a nice example of such field that may be easy to compute? | |
Nov 11, 2013 at 2:21 | comment | added | kjs | @Filipo: Thank you!! | |
Nov 11, 2013 at 1:57 | history | edited | kjs | CC BY-SA 3.0 |
added 20 characters in body
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Nov 10, 2013 at 20:41 | comment | added | Franz Lemmermeyer | @Filipo: sorry, my mistake. So the smallest counterexample would be a (2,4)-extension such that only an ideal of order 4 capitulates in the genus field. It can't be that hard to find. | |
S Nov 10, 2013 at 19:05 | history | suggested | Filippo Alberto Edoardo | CC BY-SA 3.0 |
Improved spelling and English, improved formatting.
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Nov 10, 2013 at 18:21 | review | Suggested edits | |||
S Nov 10, 2013 at 19:05 | |||||
Nov 10, 2013 at 15:44 | comment | added | Filippo Alberto Edoardo | @FranzLemmermeyer: I have downloaded the paper and read it, but found no counterexample. It seems to me that the paper only deals with the (by then not yet proved) classical principal ideal theorem in the case $Cl_k=(\mathbb{Z}/\ell)^2$, proving it. The various examples treat capitulation in the intermediate fields of degree $\ell$, but these do not fall into the OP setting. | |
Nov 10, 2013 at 12:29 | comment | added | Franz Lemmermeyer | If "can be" means "is", then there are counterexamples in Furtwängler's article from 1916 (Monatsh. f. Math. 27). | |
Nov 6, 2013 at 23:17 | review | First posts | |||
Nov 6, 2013 at 23:17 | |||||
Nov 6, 2013 at 23:00 | history | asked | kjs | CC BY-SA 3.0 |