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May 31, 2013 at 14:13 comment added Arkandias I found the answer in Landvogt's "A compactification of the Bruhat-Tits building". Thank you for your time !
May 31, 2013 at 12:34 comment added Arkandias Yes sorry for the mistakes, I wrote in a hurry. It's been corrected. I can find the proofs of the facts you mentioned. How do you deduce the result from these ?
May 31, 2013 at 12:09 history edited Arkandias CC BY-SA 3.0
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May 31, 2013 at 11:46 history edited Arkandias CC BY-SA 3.0
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May 31, 2013 at 8:50 comment added Arkandias In Tit's "Reductive groups over local fields", it is implicitly used on page 32 (see this explanation by JK Yu).
May 30, 2013 at 22:45 comment added Jim Humphreys I'm not sure where in the literature this first appears (can you document your own sources further?). But it may help to start with the case of relative rank 1, where the assertion looks more familiar. Since $S$ is just a product of multiplicative groups, maybe it's easy to generalize to higher rank. In any case, Tits himself had some early announcements and expositions before the more technical Bruhat-Tits papers appeared. I'll take a closer look.
May 30, 2013 at 20:14 history asked Arkandias CC BY-SA 3.0