Astérisque 2012; 147 pp; softcover Number: 345 ISBN10: 285629345X ISBN13: 9782856293454 List Price: US$60 Member Price: US$48 Order Code: AST/345
 On a complex manifold \((X,\mathcal{O}_X)\), a \(\mathrm{DQ}\)module is a module (in the derived sense) over an algebroid stack locally equivalent to the sheaf \(\mathcal{O}_X[[\hbar]]\) endowed with a starproduct. The book treats relative finiteness, duality and index theorems for \(\mathrm{DQ}\)modules, showing in particular the functoriality of the Hochschild class in this framework and studying in detail holonomic modules in the symplectic case. Hence, these notes could be considered both as an introduction to noncommutative complex analytic geometry and to the study of microdifferential systems on complex Poisson manifolds. A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list. Readership Graduate students and research mathematicians interested in deformation quantization, DQmodules, complex Poisson manifolds, algebroid stacks, convolution of kernels, dualizing complexes, Hochschild homology, Euler classes, and holonomic modules. Table of Contents  Modules over formal deformations
 DQalgebroids
 Kernels
 Hochschild classes
 The commutative case
 Symplectic case and \(\mathcal{D}\)modules
 Holonomic DQmodules
 Notation index
 Terminological index
 Bibliography
