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A Topological Reconstruction Theorem for $D^{\infty}$-Modules Prosmans, Fabienne ; Schneiders, Jean-Pierre in Duke Mathematical Journal (2000), 102(1), 39-86 We prove that any perfect complex of $D^{\infty}-modules may be reconstructed from its holomorphic solution complex provided that we keep track of the natural topology of this last complex. This is to be ... [more ▼] We prove that any perfect complex of $D^{\infty}-modules may be reconstructed from its holomorphic solution complex provided that we keep track of the natural topology of this last complex. This is to be compared with the reconstruction theorem for regular holonomic D-modules which follows from the well-known Riemann-Hilbert correspondence. [less ▲] Detailed reference viewed: 25 (14 ULg)Derived Categories for Functional Analysis Prosmans, Fabienne in Publications of the Research Institute for Mathematical Sciences (2000), 36(1), 19-83 We study the homological algebra of the category of locally convex topological vector spaces from the point of view of derived categories. Detailed reference viewed: 40 (18 ULg)Derived Limits in Quasi-Abelian Categories Prosmans, Fabienne in Bulletin de la Société Royale des Sciences de Liège (1999), 68(5-6), 335-401 We study the derived functors of projective limit functors in quasi-abelian categories. Detailed reference viewed: 14 (2 ULg)Derived Projective Limits of Topological Abelian Groups Prosmans, Fabienne in Journal of Functional Analysis (1999), 162(1), 135-177 We prove that the category of topological Abelian groups is quasi-Abelian. Using results about derived projective limits in quasi-Abelian categories, we study exactness properties of the projective limit ... [more ▼] We prove that the category of topological Abelian groups is quasi-Abelian. Using results about derived projective limits in quasi-Abelian categories, we study exactness properties of the projective limit functor in the category of topological Abelian groups. [less ▲] Detailed reference viewed: 19 (3 ULg) |
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