Duke Mathematical Journal

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

Annette Werner

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Abstract

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

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

Dates
First available in Project Euclid: 18 June 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1087575043

Digital Object Identifier
doi:10.1215/S0012-7094-02-11125-9

Mathematical Reviews number (MathSciNet)
MR1882137

Zentralblatt MATH identifier
1075.14022

Subjects
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

Citation

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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