A fixed point formula for varieties over finite fields.
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A fixed point formula of Lefschetz type in Arakelov geometry II: A residue formula
Kai Köhler, Damien Roessler (2002)
Annales de l’institut Fourier
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.
A geometrical approach to the theory of Jacobi forms
Jürg Kramer (1991)
Compositio Mathematica
A Grothendieck-Riemann-Roch Formula for Maps of Complex Manifolds.
Domingo Toledo, Yue Lin L. Tong, Nigel R. O'Brian (1985)
Mathematische Annalen
A proof of Noether's formula for the arithmetic genus of an algebraic surface
Ragni Piene (1979)
Compositio Mathematica
A Riemann-Roch theorem for dg algebras
François Petit (2013)
Bulletin de la Société Mathématique de France
Given a smooth proper dg algebra , a perfect dg -module and an endomorphism of , we define the Hochschild class of the pair with values in the Hochschild homology of the algebra . Our main result is a Riemann-Roch type formula involving the convolution of two such Hochschild classes.
A Riemann-Roch theorem for flat bundles, with values in the algebraic Chern-Simons theory.
Bloch, Spencer, Esnault, Hélène (2000)
Annals of Mathematics. Second Series
A singular Riemann-Roch for Hirzebruch characteristics
Shoji Yokura (1998)
Banach Center Publications
Algebraische Funktionen mit Polen in spezieller Lage.
Rainer Weissauer (1986)
Mathematische Zeitschrift
An Arakelov theoretic proof of the equality of conductor and discriminant
Sinan Ünver (2004)
Journal de Théorie des Nombres de Bordeaux
We give an Arakelov theoretic proof of the equality of conductor and discriminant.
An arithmetic Riemann-Roch theorem.
Henri Gillet, Christophe Soulé (1992)
Inventiones mathematicae
An arithmetic Riemann-Roch theorem in higher degrees
Henri Gillet, Damian Rössler, Christophe Soulé (2008)
Annales de l’institut Fourier
We prove an analog in Arakelov geometry of the Grothendieck-Riemann-Roch theorem.
An Equivariant Lefschetz Formula for Finite Reductive Groups.
G. Ellingsrud, K. Lonsted (1980)
Mathematische Annalen
An equivariant Riemann-Roch theorem for complete, simplicial toric varieties.
Michel Brion, Michèle Vergne (1997)
Journal für die reine und angewandte Mathematik
Asymptotic Morse inequalities for analytic sheaf cohomology
Yum-Tong Siu (1985/1986)
Séminaire Bourbaki
Chern classes and Hirzebruch-Riemann-Roch theorem for coherent sheaves on complex-projective orbifolds with isolated singularities.
Raimnund Blache (1996)
Mathematische Zeitschrift
Chow categories
J. Franke (1990)
Compositio Mathematica
Classes caractéristiques et théorèmes d'indice : point de vue microlocal
Claude Sabbah (1995/1996)
Séminaire Bourbaki
Complex immersions and Quillen metrics
Jean-Michel Bismut, Gilles Lebeau (1991)
Publications Mathématiques de l'IHÉS
Direct images in non-archimedean Arakelov theory
Henri Gillet, Christophe Soulé (2000)
Annales de l'institut Fourier
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.
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