Timeline for Hasse principle for rational times square

11 events

when toggle format	what		by	license	comment
Jun 16, 2016 at 4:52	answer	added	Mikhail Borovoi		timeline score: 4
Jun 14, 2016 at 18:22	vote	accept	JadeSnail
Jun 14, 2016 at 2:31	answer	added	David E Speyer		timeline score: 7
Jun 5, 2016 at 0:15	answer	added	David E Speyer		timeline score: 13
Jun 4, 2016 at 19:31	answer	added	user42024		timeline score: 8
Jun 4, 2016 at 18:10	comment	added	Mikhail Borovoi		(cont.). Let $\mathbb{L}$ denote the normal closure of $\mathbb{K}$ in $\overline{\mathbb{Q}}$, and let $G=\mathrm{Gal}(\mathbb{L}/\mathbb{Q})$. If all the Sylow subgroups of $G$ are cyclic, then the answer seem to be YES. In general I would expect the answer NO.
Jun 4, 2016 at 18:02	comment	added	Mikhail Borovoi		Consider the question in the form of GH from MO. The answer seem to depend on $\mathbb{K}$.
Jun 4, 2016 at 16:01	comment	added	GH from MO		Concerning the edit, the necessary condition needs to be strengthened as a whole (not just at the real places of $\mathbb{K}$): for any place $u$ of $\mathbb{Q}$, there is $q\in\mathbb{Q}$ such that for any place $v$ of $\mathbb{K}$ lying above $u$, we have $a=qk^2$ for some $k\in\mathbb{K}_v$. In fact the assumption $q\in\mathbb{Q}$ could be relaxed to the more natural condition $q\in\mathbb{Q}_u$.
Jun 4, 2016 at 15:24	history	edited	Mikhail Borovoi		tags added
Jun 4, 2016 at 15:02	history	edited	JadeSnail	CC BY-SA 3.0	added 142 characters in body
Jun 4, 2016 at 14:20	history	asked	JadeSnail	CC BY-SA 3.0