Timeline for Countability of conjugacy classes of closed subgroups

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10 events

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Apr 18, 2017 at 21:27	history	edited	Uri Bader	CC BY-SA 3.0	added 43 characters in body
Apr 18, 2017 at 21:11	history	edited	Uri Bader	CC BY-SA 3.0	added 3814 characters in body
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Apr 12, 2017 at 11:08	history	edited	YCor	CC BY-SA 3.0	specified target in links
Apr 12, 2017 at 10:51	history	edited	Uri Bader	CC BY-SA 3.0	added 2118 characters in body
Apr 11, 2017 at 16:09	comment	added	Uri Bader		Thanks, Yves. Actually, I also thought of using Borel-Serre and the analogous complex result. I would, if I have found a simpler proof going this way, but I have not. So, if anyway giving the local-rigidity proof, why not providing a stronger result (one should be able to replace $\mathbb{R}$ with any local field)?
Apr 11, 2017 at 15:42	comment	added	YCor		I'd expect that there is a similar sketch, but possibly slightly simpler, based on (1) Every complex reductive group has countably many conjugacy classes of (complex) reductive subgroups. It is easy to deduce the result since the $\mathbf{R}$-points of a transitive $G$-set has finitely many $G(\mathbf{R})$-orbits (Borel-Serre). As there are countably many reductive groups, (1) follows from (2): for all $H,G$ complex reductive, $Hom(H,G)$ has countably many classes (up to $G$-conjugacy). (2) seems to follow from your approach, but the whole avoids passing to $\bar{\mathbf{Q}}$-points.
Apr 11, 2017 at 14:16	history	edited	Uri Bader	CC BY-SA 3.0	added 2857 characters in body
Apr 10, 2017 at 9:25	history	answered	Uri Bader	CC BY-SA 3.0