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Vector bundles. --- D-modules. --- Fibrés vectoriels. --- D-modules, Théorie des.
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D-modules --- Holonomy groups --- D-modules, Théorie des. --- Groupes d'holonomie.
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Analytical spaces --- Algebraic geometry --- Differential geometry. Global analysis --- 51 <082.1> --- Mathematics--Series --- Hodge theory --- D-modules --- Vector bundles --- Harmonic maps --- Applications harmoniques --- Fibrés vectoriels --- D-modules, Théorie des --- Hodge, Théorie de --- Applications harmoniques. --- Fibrés vectoriels. --- D-modules, Théorie des. --- Hodge, Théorie de.
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Sheaf theory. --- Induction (Mathematics) --- Abelian categories. --- Sheaf theory --- Integral transforms --- D-modules --- Faisceaux, Théorie des. --- Transformations intégrales. --- D-modules, Théorie des. --- Faisceaux, Théorie des. --- Transformations intégrales. --- D-modules, Théorie des.
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"D-module theory is essentially the algebraic study of systems of linear partial differential equations. This book, the first devoted specifically to holonomic D-modules, provides a unified treatment of both regular and irregular D-modules. The authors begin by recalling the main results of the theory of indsheaves and subanalytic sheaves, explaining in detail the operations on D-modules and their tempered holomorphic solutions. As an application, they obtain the Riemann-Hilbert correspondence for regular holonomic D-modules. In the second part of the book the authors do the same for the sheaf of enhanced tempered solutions of (not necessarily regular) holonomic D-modules. Originating from a series of lectures given at the Institut des Hautes Études Scientifiques in Paris, this book is addressed to graduate students and researchers familiar with the language of sheaves and D-modules, in the derived sense." [Publisher]
D-modules. --- D-modules, Théorie des. --- Modules (Algebra) --- Modules (algèbre) --- Sheaf theory. --- Faisceaux, Théorie des. --- Geometry, Algebraic. --- Géométrie algébrique. --- D-modules, Théorie des. --- Modules (algèbre) --- Faisceaux, Théorie des. --- Géométrie algébrique.
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D-modules continues to be an active area of stimulating research in such mathematical areas as algebra, analysis, differential equations, and representation theory. Key to D-modules, Perverse Sheaves, and Representation Theory is the authors' essential algebraic-analytic approach to the theory, which connects D-modules to representation theory and other areas of mathematics. Significant concepts and topics that have emerged over the last few decades are presented, including a treatment of the theory of holonomic D-modules, perverse sheaves, the all-important Riemann-Hilbert correspondence, Hodge modules, and the solution to the Kazhdan-Lusztig conjecture using D-module theory. To further aid the reader, and to make the work as self-contained as possible, appendices are provided as background for the theory of derived categories and algebraic varieties. The book is intended to serve graduate students in a classroom setting and as self-study for researchers in algebraic geometry, and representation theory.
Ordered algebraic structures --- Geometry --- algebra --- topologie (wiskunde) --- Topological groups. Lie groups --- Algebra --- landmeetkunde --- wiskunde --- Group theory --- Représentations d'algèbres de Lie --- Representations of Lie algebras --- Linear algebraic groups. --- D-modules. --- Representations of groups. --- Groupes algébriques linéaires --- D-modules, Théorie des --- Représentations de groupes
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