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Le théorème de continuité de la division dans les anneaux d'opérateurs différentiels

 

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Author: Mebkhout, Zoghman
Narváez Macarro, Luis
Department: Universidad de Sevilla. Departamento de álgebra
Date: 1998
Published in: Journal für die reine und angewandte Mathematik, 503, 193-236.
Document type: Article
Abstract: In this paper we prove the continuity of Weierstrass-Hironaka division of finite order linear differential operators over a complex analytic manifold X with respect to the induced topology by a canonical one of Fréchet nuclear on the sheaf script D∞X. As a consequence, admissible modules over script D∞X and coherent modules over script DX inherit a canonical locally convex structure and admit finite free resolutions with strict morphisms. This structure allows, as example, to give a topological caracterisation of regularity and to prove that the existence of a regular Bernstein-Sato functional equation for a coherent script DX-module, M, with respect to an arbitrary divisor Y ⊂ X, implies the comparison theorem script D∞X ⊗script DX M[*Y] ≃ j*j-1 M∞.
Cite: Mebkhout, Z. y Narváez Macarro, L. (1998). Le théorème de continuité de la division dans les anneaux d'opérateurs différentiels. Journal für die reine und angewandte Mathematik, 503, 193-236.
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URI: http://hdl.handle.net/11441/46774

DOI: 10.1515/crll.1998.097

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