A fixed point formula of Lefschetz type in Arakelov geometry II: A residue formula

Kai Köhler[1]; Damien Roessler[2]

  • [1] Mathematisches Institut, Einsteinstr. 62, 48149 Münster (Allemagne)
  • [2] ETH-Zentrum, Mathematik Department, 8092 Zurich (Suisse)

Annales de l’institut Fourier (2002)

  • Volume: 52, Issue: 1, page 81-103
  • ISSN: 0373-0956

Abstract

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This is the second of a series of papers dealing with an analog in Arakelov geometry of the holomorphic Lefschetz fixed point formula. We use the main result of the first paper to prove a residue formula "à la Bott" for arithmetic characteristic classes living on arithmetic varieties acted upon by a diagonalisable torus; recent results of Bismut- Goette on the equivariant (Ray-Singer) analytic torsion play a key role in the proof.

How to cite

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Köhler, Kai, and Roessler, Damien. "A fixed point formula of Lefschetz type in Arakelov geometry II: A residue formula." Annales de l’institut Fourier 52.1 (2002): 81-103. <http://eudml.org/doc/115981>.

@article{Köhler2002,
abstract = {This is the second of a series of papers dealing with an analog in Arakelov geometry of the holomorphic Lefschetz fixed point formula. We use the main result of the first paper to prove a residue formula "à la Bott" for arithmetic characteristic classes living on arithmetic varieties acted upon by a diagonalisable torus; recent results of Bismut- Goette on the equivariant (Ray-Singer) analytic torsion play a key role in the proof.},
affiliation = {Mathematisches Institut, Einsteinstr. 62, 48149 Münster (Allemagne); ETH-Zentrum, Mathematik Department, 8092 Zurich (Suisse)},
author = {Köhler, Kai, Roessler, Damien},
journal = {Annales de l’institut Fourier},
keywords = {Arakelov; analytic torsion; Bott; fixed point formula; height; Hermitian bundle; arithmetic Bott residue formula; arithmetic Lefschetz fixed point formula; arithmetic Riemann-Roch theorem; arithmetic Chern number; anomaly term; characteristic current; Arakelov geometry},
language = {eng},
number = {1},
pages = {81-103},
publisher = {Association des Annales de l'Institut Fourier},
title = {A fixed point formula of Lefschetz type in Arakelov geometry II: A residue formula},
url = {http://eudml.org/doc/115981},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Köhler, Kai
AU - Roessler, Damien
TI - A fixed point formula of Lefschetz type in Arakelov geometry II: A residue formula
JO - Annales de l’institut Fourier
PY - 2002
PB - Association des Annales de l'Institut Fourier
VL - 52
IS - 1
SP - 81
EP - 103
AB - This is the second of a series of papers dealing with an analog in Arakelov geometry of the holomorphic Lefschetz fixed point formula. We use the main result of the first paper to prove a residue formula "à la Bott" for arithmetic characteristic classes living on arithmetic varieties acted upon by a diagonalisable torus; recent results of Bismut- Goette on the equivariant (Ray-Singer) analytic torsion play a key role in the proof.
LA - eng
KW - Arakelov; analytic torsion; Bott; fixed point formula; height; Hermitian bundle; arithmetic Bott residue formula; arithmetic Lefschetz fixed point formula; arithmetic Riemann-Roch theorem; arithmetic Chern number; anomaly term; characteristic current; Arakelov geometry
UR - http://eudml.org/doc/115981
ER -

References

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