Translator Disclaimer
1 February 2002 Arakelov intersection indices of linear cycles and the geometry of buildings and symmetric spaces
Annette Werner
Duke Math. J. 111(2): 319-355 (1 February 2002). DOI: 10.1215/S0012-7094-02-11125-9

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.

Citation

Download Citation

Annette Werner. "Arakelov intersection indices of linear cycles and the geometry of buildings and symmetric spaces." Duke Math. J. 111 (2) 319 - 355, 1 February 2002. https://doi.org/10.1215/S0012-7094-02-11125-9

Information

Published: 1 February 2002
First available in Project Euclid: 18 June 2004

zbMATH: 1075.14022
MathSciNet: MR1882137
Digital Object Identifier: 10.1215/S0012-7094-02-11125-9

Subjects:
Primary: 14G40
Secondary: 14C17 , 20E42 , 51E24

Rights: Copyright © 2002 Duke University Press

JOURNAL ARTICLE
37 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.111 • No. 2 • 1 February 2002
Back to Top