Duke Mathematical Journal

Arakelov intersection indices of linear cycles and the geometry of buildings and symmetric spaces

Annette Werner

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This paper generalizes Yu. Manin's approach toward a geometrical interpretation of Arakelov theory at infinity to linear cycles in projective spaces. We show how to interpret certain non-Archimedean Arakelov intersection numbers of linear cycles on ∙n−1 with the combinatorial geometry of the Bruhat-Tits building associated to PGL(n)$. This geometric setting has an Archimedean analogue, namely, the Riemannian symmetric space associated to SL(n,ℂ), which we use to interpret analogous Archimedean intersection numbers of linear cycles in a similar way.

Article information

Duke Math. J., Volume 111, Number 2 (2002), 319-355.

First available in Project Euclid: 18 June 2004

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Zentralblatt MATH identifier

Primary: 14G40: Arithmetic varieties and schemes; Arakelov theory; heights [See also 11G50, 37P30]
Secondary: 14C17: Intersection theory, characteristic classes, intersection multiplicities [See also 13H15] 20E42: Groups with a $BN$-pair; buildings [See also 51E24] 51E24: Buildings and the geometry of diagrams


Werner, Annette. Arakelov intersection indices of linear cycles and the geometry of buildings and symmetric spaces. Duke Math. J. 111 (2002), no. 2, 319--355. doi:10.1215/S0012-7094-02-11125-9. https://projecteuclid.org/euclid.dmj/1087575043

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