Timeline for How locally ubiquitous are totally real fields?
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| Apr 27, 2011 at 18:22 | comment | added | fherzig | @Alex: Thanks for checking, that makes sense that they deal with cyclic extensions only. | |
| Apr 27, 2011 at 13:06 | comment | added | Alex B. | @Florian Thank you for the extra references. In Artin-Tate, I have found Theorem 5 on page 105, which deals with cyclic extensions. | |
| Apr 27, 2011 at 12:24 | comment | added | fherzig | There is a more precise lemma in Clozel-Harris-Taylor, still with a short and simple proof; see lemma 4.1.2. It constructs a solvable Galois extension with prescribed completions at finitely many places (incl. the real place) that is linearly disjoint from any given finite Galois extension. I think there's another precise version which lets you prescribe the global degree (subject to constraints arising from Grünwald-Wang) in Artin-Tate, section on G-W. [I don't have the book with me to give you a precise reference.] | |
| Apr 27, 2011 at 9:38 | vote | accept | Torsten Wedhorn | ||
| Apr 27, 2011 at 6:35 | history | edited | Alex B. | CC BY-SA 3.0 |
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| Apr 27, 2011 at 6:20 | history | answered | Alex B. | CC BY-SA 3.0 |