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

Köhler, Kai; Roessler, Damien

Annales de l'Institut Fourier, Tome 52 (2002) no. 1, pp. 81-103.

Cet article est le second d'une série, dont l'objet est un analogue en géométrie d'Arakelov de la formule du point fixe de Lefschetz holomorphe. Nous utilisons le résultat principal du premier article pour prouver une formule des résidus "à la Bott" pour des classes caractéristiques existant sur des variétés arithmétiques munies d'une action de tore; de récents résultats de Bismut-Goette sur la torsion analytique équivariante (de Ray-Singer) jouent un rôle clé dans la preuve.

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.

Classification : 14G40, 58J52, 14C40, 14L30, 58J20, 14K15
Keywords: Arakelov, analytic torsion, Bott, fixed point formula, height, Hermitian bundle
Mot clés : Arakelov, torsion analytique, Bott, formule du point fixe, hauteur, fibré hermitien

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