Non-archimedean intersection indices on projective spaces and the Bruhat-Tits building for P G L

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

Abstract

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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 ℙ n - 1 with the combinatorial geometry of the Bruhat-Tits building associated to P G L ( n ) .

How to cite

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Werner, 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

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

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