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𝒟 -modules micro-localement libres de rang 1 et connexions non-intégrables en dimension 2

Matthieu Carette (2002)

Annales de l’institut Fourier

Dans un article sur la transformation de Radon-Penrose, A. D’Agnolo et P. Schapira ont montré qu’au-dessus d’une variété complexe X de dimension 3 , tout ^ - module localement libre de rang 1 est de la forme ^ π - 1 𝒪 π - 1 pour un fibré inversible sur X . Ce résultat est faux en dimension 2 , et le but de ce travail est de déterminer la structure des 𝒟 - modules micro-localement libres de rang 1 dans ce cas. Un des principaux résultat est la description des 𝒟 -modules micro-localement libres de rang un en termes...

A Riemann-Roch-Hirzebruch formula for traces of differential operators

Markus Engeli, Giovanni Felder (2008)

Annales scientifiques de l'École Normale Supérieure

Let D be a holomorphic differential operator acting on sections of a holomorphic vector bundle on an n -dimensional compact complex manifold. We prove a formula, conjectured by Feigin and Shoikhet, giving the Lefschetz number of D as the integral over the manifold of a differential form. The class of this differential form is obtained via formal differential geometry from the canonical generator of the Hochschild cohomology H H 2 n ( 𝒟 n , 𝒟 n * ) of the algebra of differential operators on a formal neighbourhood of a...

Continuous division of differential operators

Herwig Hauser, Luis Narváez-Macarro (2001)

Annales de l’institut Fourier

In this paper, we give a new proof of the continuity of division by differential operators with analytic coefficients, originally proved by Mebkhout and the second author. Our methods come from the proof of the Constant Rank Theorem for analytic maps between power series spaces, given by Müller and the first author.

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