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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

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.

The Chern character for Lie-Rinehart algebras

Helge Maakestad (2005)

Annales de l'institut Fourier

Let A be a commutative S -algebra where S is a ring containing the rationals. We prove the existence of a Chern character for Lie-Rinehart algebras L over A with values in the Lie-Rinehart cohomology of L which is independent of choice of a L -connection. Our result generalizes the classical Chern character from the K -theory of A to the algebraic De Rham cohomology.

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