Non-Archimedean intersection indices on projective spaces and the   Bruhat-Tits building for PGL
  Inspired by Manin's approach towards a geometric interpretation of Arakelov theory at infinity, we interpret in this paper non-Archimedean local intersection numbers of linear cycles in $P^{n-1}$ with the combinatorial geometry of the Bruhat-Tits building associated to PGL(n). 
Annette Werner