Displaying similar documents to “An arithmetic Riemann-Roch theorem in higher degrees”

Direct images in non-archimedean Arakelov theory

Henri Gillet, Christophe Soulé (2000)

Annales de l'institut Fourier

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We develop a formalism of direct images for metrized vector bundles in the context of the non-archimedean Arakelov theory introduced in our joint work with S. Bloch. We prove a Riemann-Roch-Grothendieck theorem for this direct image.

The arithmetic Grothendieck-Riemann-Roch theorem for general projective morphisms

José Ignacio Burgos Gil, Gerard Freixas i Montplet, Răzvan Liţcanu (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

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In this paper we extend the arithmetic Grothendieck-Riemann-Roch Theorem to projective morphisms between arithmetic varieties that are not necessarily smooth over the complex numbers. The main ingredient of this extension is the theory of generalized holomorphic analytic torsion classes previously developed by the authors.

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

Kai Köhler, Damien Roessler (2002)

Annales de l’institut Fourier

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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.

On the arithmetic Chern character

H. Gillet, C. Soulé (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

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We consider a short sequence of hermitian vector bundles on some arithmetic variety. Assuming that this sequence is exact on the generic fiber we prove that the alternated sum of the arithmetic Chern characters of these bundles is the sum of two terms, namely the secondary Bott Chern class of the sequence and its Chern character with support on the finite fibers. Next, we compute these classes in the situation encountered by the second author when proving a “Kodaira vanishing...