Timeline for If L is a field extension of K, how big is L/K?

10 events

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Mar 15, 2012 at 20:24	history	edited	Guntram	CC BY-SA 3.0	deleted 1 characters in body
Mar 15, 2012 at 20:21	comment	added	Joe Silverman		A similar, and extremely interesting, question, is the structure of $K^{\times}/N_{L/K}L^{\times}$ and its relation to $G(L\cap K^{ab}/K)$, where $L\cap K^{ab}$ is the maximal abelian extension of $K$ contained in $L$. (Probably you already know this, but I thought I'd mention it in case you didn't.)
Mar 15, 2012 at 18:29	answer	added	Marc Palm		timeline score: 1
Mar 18, 2010 at 6:51	vote	accept	Guntram
Mar 16, 2010 at 17:16	answer	added	Bjorn Poonen		timeline score: 9
Mar 16, 2010 at 14:15	answer	added	Franz Lemmermeyer		timeline score: 14
Mar 16, 2010 at 14:15	comment	added	Chandan Singh Dalawat		When $K=\mathbb{Q}_p$ (where $p$ is a prime) and the extension is of degree $[L:K]>1$, the group $L^\times/K^\times$ is uncountable.
Mar 16, 2010 at 14:12	history	edited	Guntram		added tag
Mar 16, 2010 at 14:10	comment	added	t3suji		Let's look at the more familiar example $L=\mathbb{Q}(\sqrt{-1})$, $K=\mathbb{Q}$. It is easy to see that $L^\times/K^\times$ is not finitely generated. Indeed, $L^\times$ is the sum of copies of $\mathbb{Z}$ indexed by prime Gaussian integers, $K^\times$ is the sum of copies of $\mathbb{Z}$ indexed by prime integers; since infinitely many primes split in Gaussian integers, you get the result.
Mar 16, 2010 at 14:00	history	asked	Guntram	CC BY-SA 2.5

Timeline for If L is a field extension of K, how big is L*/K*?