Non-archimedean intersection indices on projective spaces and the Bruhat-Tits building for PGL
Annales de l'Institut Fourier, Volume 51 (2001) no. 6, pp. 1483-1505.

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 n-1 with the combinatorial geometry of the Bruhat-Tits building associated to PGL(n).

Nous interprétons les nombres d’intersection non archimédiens des cycles linéaires sur n-1 avec la géométrie combinatoire de l’immeuble de Bruhat-Tits associé à PGL(n). Ces résultats sont inspirés par le travail de Manin donnant une interprétation géométrique de la théorie d’Arakelov aux places infinies pour les courbes.

DOI: 10.5802/aif.1862
Classification: 14C17,  14M15,  20E42
Keywords: intersection theory, projective spaces, Bruhat-Tits building
Werner, Annette 1

1 Universität Münster, Mathematisches Institut, Einsteinstr. 62, 48149 Münster (Germany)
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Werner, Annette. Non-archimedean intersection indices on projective spaces and the Bruhat-Tits building for $PGL$. Annales de l'Institut Fourier, Volume 51 (2001) no. 6, pp. 1483-1505. doi : 10.5802/aif.1862. http://archive.numdam.org/articles/10.5802/aif.1862/

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