A fixed point formula for varieties over finite fields.
A fixed point formula of Lefschetz type in Arakelov geometry II: A residue formula
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
A Grothendieck-Riemann-Roch Formula for Maps of Complex Manifolds.
A proof of Noether's formula for the arithmetic genus of an algebraic surface
A Riemann-Roch theorem for dg algebras
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.
A singular Riemann-Roch for Hirzebruch characteristics
Algebraische Funktionen mit Polen in spezieller Lage.
An Arakelov theoretic proof of the equality of conductor and discriminant
We give an Arakelov theoretic proof of the equality of conductor and discriminant.
An arithmetic Riemann-Roch theorem.
An arithmetic Riemann-Roch theorem in higher degrees
We prove an analog in Arakelov geometry of the Grothendieck-Riemann-Roch theorem.
An Equivariant Lefschetz Formula for Finite Reductive Groups.
An equivariant Riemann-Roch theorem for complete, simplicial toric varieties.
Asymptotic Morse inequalities for analytic sheaf cohomology
Chern classes and Hirzebruch-Riemann-Roch theorem for coherent sheaves on complex-projective orbifolds with isolated singularities.
Chow categories
Classes caractéristiques et théorèmes d'indice : point de vue microlocal
Complex immersions and Quillen metrics
Direct images in non-archimedean Arakelov theory
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.