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Let $G$ a semisimple group over $k$ and $k$ algebraically closed.

Let $G(k((t)))$ the corresponding ind-scheme, does it satisfies the Jacobson property, say closed points are dense in it?

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There is something deeply ironic about asking for the Jacobson property of the topological space which you already denote by what is actually its set of closed point. Anyway, just read 10.1 in EGA IV$_4$ for an affirmative answer (use the criterion in 10.1.2(a)). –  user61789 Jun 29 '13 at 15:00
    
Should have written IV$_3$ above. –  user61789 Jun 29 '13 at 19:25
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