Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Bruhat-Tits theory over a higher dimensional base   Let $\mathcal O_{_n} := k[[z_{_1}, \ldots, z_{_n}]]$ over an algebraically
closed residue field $k$ of characteristic zero. Set $K_{_n} :=
\text{Fract}~\mathcal O_{_n}$. Let $G$ be an almost-simple, simply-connected
affine algebraic group over $k$ with a maximal torus $T$. Given a $n$-tuple
${\bf f} = (f_{_1}, \ldots, f_{_n})$ of concave functions on the root system of
$G$ as in Bruhat-Tits \cite{bruhattits1}, \cite{bruhattits}, we define {\it
{\tt n}-bounded subgroups ${\tt P}_{_{\bf f}}(k)\subset G(K_{_n})$} as a direct
generalization of Bruhat-Tits groups for the case $n=1$. We show that these
groups are {\it schematic}, i.e. they are valued points of smooth quasi-affine
group schemes with connected fibres. This provides a higher-dimensional
analogue of the Bruhat-Tits group schemes with natural specialization
properties. Under suitable {\em tameness assumptions}, we extend all these
results replacing $\mathcal O_{_n}$ by ${\mathcal O}[[x_{_1},\cdots,x_{_n}]]$
where $\mathcal O$ is a complete discrete valuation ring with residue field of
characteristic $p$. In the last part of the paper we give applications to
constructing certain natural group schemes on wonderful embeddings of groups
and also certain families of {\tt 2-parahoric} group schemes on minimal
resolutions of surface singularities.

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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: cs