Non-archimedean intersection indices on projective spaces and the Bruhat-Tits building for PGL
Annales de l'Institut Fourier, Volume 51 (2001) no. 6, p. 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 : https://doi.org/10.5802/aif.1862
Classification:  14C17,  14M15,  20E42
Keywords: intersection theory, projective spaces, Bruhat-Tits building
@article{AIF_2001__51_6_1483_0,
     author = {Werner, Annette},
     title = {Non-archimedean intersection indices on projective spaces and the Bruhat-Tits building for $PGL$},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {51},
     number = {6},
     year = {2001},
     pages = {1483-1505},
     doi = {10.5802/aif.1862},
     zbl = {1054.14030},
     mrnumber = {1870636},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2001__51_6_1483_0}
}
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://www.numdam.org/item/AIF_2001__51_6_1483_0/

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