# Non-archimedean intersection indices on projective spaces and the Bruhat-Tits building for $PGL$

Annette Werner^{[1]}

- [1] Universität Münster, Mathematisches Institut, Einsteinstr. 62, 48149 Münster (Germany)

Annales de l’institut Fourier (2001)

- Volume: 51, Issue: 6, page 1483-1505
- ISSN: 0373-0956

## Access Full Article

top## Abstract

top## How to cite

topWerner, Annette. "Non-archimedean intersection indices on projective spaces and the Bruhat-Tits building for $PGL$." Annales de l’institut Fourier 51.6 (2001): 1483-1505. <http://eudml.org/doc/115955>.

@article{Werner2001,

abstract = {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 $\{\mathbb \{P\}\}^\{n-1\}$ with the combinatorial geometry of the Bruhat-Tits building
associated to $PGL(n)$.},

affiliation = {Universität Münster, Mathematisches Institut, Einsteinstr. 62, 48149 Münster (Germany)},

author = {Werner, Annette},

journal = {Annales de l’institut Fourier},

keywords = {intersection theory; projective spaces; Bruhat-Tits building; local intersection numbers; Serre's intersection number},

language = {eng},

number = {6},

pages = {1483-1505},

publisher = {Association des Annales de l'Institut Fourier},

title = {Non-archimedean intersection indices on projective spaces and the Bruhat-Tits building for $PGL$},

url = {http://eudml.org/doc/115955},

volume = {51},

year = {2001},

}

TY - JOUR

AU - Werner, Annette

TI - Non-archimedean intersection indices on projective spaces and the Bruhat-Tits building for $PGL$

JO - Annales de l’institut Fourier

PY - 2001

PB - Association des Annales de l'Institut Fourier

VL - 51

IS - 6

SP - 1483

EP - 1505

AB - 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 ${\mathbb {P}}^{n-1}$ with the combinatorial geometry of the Bruhat-Tits building
associated to $PGL(n)$.

LA - eng

KW - intersection theory; projective spaces; Bruhat-Tits building; local intersection numbers; Serre's intersection number

UR - http://eudml.org/doc/115955

ER -

## References

top- F. Bruhat, J. Tits, Groupes réductifs sur un corps local. I. Données radicielles valuées, Publ. Math. IHES 41 (1972), 5-252 Zbl0254.14017MR327923
- W. Fulton, Intersection theory, (1998), Springer Zbl0885.14002MR1644323
- H. Gillet, C. Soulé, Arithmetic intersection theory, Publ. Math. IHES 72 (1990), 93-174 Zbl0741.14012MR1087394
- Y.I. Manin, Three-dimensional hyperbolic geometry as $\infty $-adic Arakelov geometry, Invent. Math. 104 (1991), 223-244 Zbl0754.14014MR1098608
- J.-P. Serre, Algèbre locale. Multiplicités, 11 (1965), Springer Zbl0142.28603MR201468
- A. Werner, Arakelov intersection indices of linear cycles and the geometry of buildings and symmetric spaces Zbl1075.14022MR1882137

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.