On Grothendieck's pairing of component groups in the semistable reduction case.
Local heights on Momford curves.
A tropical view on Bruhat-Tits buildings and their compactifications
We relate some features of Bruhat-Tits buildings and their compactifications to tropical geometry. If G is a semisimple group over a suitable non-Archimedean field, the stabilizers of points in the Bruhat-Tits building of G and in some of its compactifications are described by tropical linear algebra. The compactifications we consider arise from algebraic representations of G. We show that the fan which is used to compactify an apartment in this theory is given by the weight polytope of the representation...
Non-archimedean intersection indices on projective spaces and the Bruhat-Tits building for
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 with the combinatorial geometry of the Bruhat-Tits building associated to .
Vector bundles on p-adic curves and parallel transport
Bruhat-Tits theory from Berkovich’s point of view. I. Realizations and compactifications of buildings
We investigate Bruhat-Tits buildings and their compactifications by means of Berkovich analytic geometry over complete non-Archimedean fields. For every reductive group over a suitable non-Archimedean field we define a map from the Bruhat-Tits building to the Berkovich analytic space associated with . Composing this map with the projection of to its flag varieties, we define a family of compactifications of . This generalizes results by Berkovich in the case of split groups. Moreover,...
Local heights on Abelian varieties and rigid analytic uniformization.
Compactification of the Bruhat-Tits building of PGL by lattices of smaller rank.
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