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Tagged with arithmetic-groups arithmetic-geometry
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$K$-ranks of some algebraic groups in Lubotzky's "Discrete groups, expanding graphs and invariant measures"
$\DeclareMathOperator\SL{SL}\DeclareMathOperator\SO{SO}$Let $G$ be a semisimple algebraic group and $K$ any field. Then
the $K$-rank of $G$ is the maximal rank $r$ of a $K$-splitting
torus $T \cong (K^...
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Compactifications of group schemes
Let $G$ be a group scheme over a scheme $S$ which is the spectrum of a discrete valuation ring. Let $\eta$ (resp. $s$) be the generic (resp. closed) point. Assume that the generic fiber $G_{\eta}$ is ...
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