Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Wonderful compactifications of Bruhat-Tits buildings in the non-split
  case   Given an adjoint semisimple group $G$ over a local field $k$, we prove that
the maximal Satake-Berkovich compactification of the Bruhat-Tits building of
$G$ can be identified with the one obtained by embedding the building into the
Berkovich analytification of the wonderful compactification of $G$, extending
previous results of R\'emy, Thuillier and Werner. In the process, we use the
characterisation of the wonderful compactification in terms of Hilbert schemes
given by Brion to extend the definition of the wonderful compactification to
the case of a non-necessarily split adjoint semisimple group over an arbitrary
field and investigate some of its properties pertaining to rational points on
the boundary.
  Lastly, given a finite possibly ramified Galois extension $k'/k$, we take a
look at the action of the Galois group on the maximal compactification of the
building of $G$ over $k'$ and check that the Galois-fixed points are precisely
the limits of sequences of fixed points in the building over $k'$, though they
may not lie in the Satake-Berkovich compactification of $G$ over $k$.

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The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: physics