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Kai Köhler; Damien Roessler
A fixed point formula of Lefschetz type in Arakelov geometry II: A residue formula
(Une formule du point fixe de type Lefschetz en géométrie d'Arakelov II : une formule des résidus)
Annales de l'institut Fourier, 52 no. 1 (2002), p. 81-103, doi: 10.5802/aif.1877
Article PDF | Reviews MR 1881571 | Zbl 1001.14006
Class. Math.: 14G40, 58J52, 14C40, 14L30, 58J20, 14K15
Keywords: Arakelov, analytic torsion, Bott, fixed point formula, height, Hermitian bundle

Résumé - 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.

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