Buildings Algebraic_torus

if




g



{\displaystyle \mathbf {g} }

semisimple group on





q


p




{\displaystyle \mathbb {q} _{p}}

maximal split tori in




g



{\displaystyle \mathbf {g} }

correspond apartments of bruhat-tits building



x


{\displaystyle x}

associated




g



{\displaystyle \mathbf {g} }

. in particular dimension of



x


{\displaystyle x}

equal





q


p




{\displaystyle \mathbb {q} _{p}}

-rank of




g



{\displaystyle \mathbf {g} }

.