Is there any way to get on top of the procedure for constructing Bruhat-Tits buildings for non-split groups over a non-archimedean local field $k$, by Galois descent, other than reading both the Bruhat-Tits articles "Groupes réductifs sur un corps local"? In particular is there any exposition which is written in English?
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2 Answers
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Jiu-Kang Yu has an article "Bruhat-Tits Theory and Buildings" which has appeared in "Ottawa Lectures on Admissible Representations of Reductive $p$-adic Groups". It doesn't directly address your question, instead it contains a guide to the literature on Bruhat-Tits buildings.
There is a 26 page pdf version of Yu's article. The published version contains a bit more information, but not a lot more (a few more references are added, plus a short introduction, plus the typesetting is updated). Unfortunately the printed version is hard to find.
answered Jun 23, 2015 at 10:48
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$\begingroup$ The published version shouldn't be that hard to find--most libraries should have it, and it's not a bad book to purchase. (That said, my copy is not on hand, so I can't compare them now.) $\endgroup$– KimballCommented Jun 23, 2015 at 12:57
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1$\begingroup$ In my experience most libraries do not have this book, and I've never seen an electronic version. Thus, hard to find. $\endgroup$ Commented Jun 25, 2015 at 6:49
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$\begingroup$ The above link to Yu's article is not working anymore, but there is one on the Internet Archive: web.archive.org/web/20210506181845/https://… $\endgroup$ Commented Jan 7, 2023 at 11:42
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There is a forthcoming book "Descent in buildings" by Bernhard Mühlherr, Holger Petersson and Richard Weiss, which should appear soon (published by Princeton University Press). See http://press.princeton.edu/titles/10649.html. It addresses exactly this issue, from a very building-theoretical point of view.
answered Jun 23, 2015 at 10:53