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Feb 25, 2011 at 13:36 comment added genshin for the second question, the case when $G'=T$ being a $\mathbb{Q}$-torus is different. Say one has a point $x$ in $X$ such that $x(\mathbb{S})\subset T_\mathbb{R}$ for some $\mathbb{Q}$-torus $T$ in $G$, which is also minimal for such inclusions, then $(T,x)$ is necessarily unique up to isomorphism: if $(T,x')$ is a second subdatum , then $x$ is conjugate to $x'$ by some $g\in G(\mathbb{R})$, and $g$ should stabilize $T$ under the assumption of existence.
Feb 25, 2011 at 13:31 history edited genshin CC BY-SA 2.5
added 1825 characters in body; edited title
Feb 22, 2011 at 19:30 vote accept genshin
Feb 22, 2011 at 19:57
Feb 22, 2011 at 17:54 answer added Mikhail Borovoi timeline score: 7
Feb 22, 2011 at 15:18 history edited genshin CC BY-SA 2.5
edited title
Feb 22, 2011 at 8:20 history asked genshin CC BY-SA 2.5