Algebraic D-modules

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Academic Press, 1987 - Mathematics - 355 pages
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Presented here are recent developments in the algebraic theory of D-modules. The book contains an exposition of the basic notions and operations of D-modules, of special features of coherent, holonomic, and regular holonomic D-modules, and of the Riemann-Hilbert correspondence. The theory of Algebraic D-modules has found remarkable applications outside of analysis proper, in particular to infinite dimensional representations of semisimple Lie groups, to representations of Weyl groups, and to algebraic geometry.

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Contents

CATEGORIES DERIVEES ET FONCTEURS DERIVES
3
2 Les catégories triangulées
26
3 La catégorie CA
36
S5 La catégorie KA
44
6 La catégorie DA
52
7 Les résolutions
70
l0 Les foncteurs dérivés de HonT
98
l2 Les classes génératrices de DbA
107
3 Inverse and direct images of Anmodules under polynomial
191
Bibliographical note
205
2 Construction of resolutions Two equivalences of categories
219
3 Left and right Pmodules
226
4 Inverse images
232
5 Direct images
240
6 Composition of direct images
249
8 Some applications
265

2 Basic theorems on coherent 0modules
115
4 Coherent Pmodules and good filtrations
121
References
127
IN DIMENSION ONE FUCHS THEORY
129
2 Reformulation in terms of meromorphic connections
141
Bibliography
149
4 Divisors with normal crossings
157
5 The RiemannHilbert correspondence
166
THE WEYL ALGEBRA
173
2 Some homological algebra
183
COHERENT HOLONOMIC AND REGULAR HOLONOMIC COMPLEXES
271
l0 Holonomic complexes
292
ll Regular holonomic complexes
301
l2 Preservation of regular holonomicity
308
THE RIEMANNHILBERT CORRESPONDENCE
321
DR i r ttS DR
330
l8 Proof of DR tr tt DR for F regular holonomic
336
20 Proof of l4 52 3 for holonomic complexes
344
22 Regular holonomic modules and perverse sheaves
350
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