Astérisque 2005; 208 pp; softcover Number: 300 ISBN10: 2856291740 ISBN13: 9782856291740 List Price: US$66 Individual Members: US$59.40 Order Code: AST/300
 In this book, the author proves a decomposition theorem for the direct image of an irreducible local system on a smooth complex projective variety under a morphism with values in another smooth complex projective variety. For this purpose, he constructs a category of polarized twistor \(\mathcal {D}\)modules and shows a decomposition theorem in this category. The book is suitable for graduate students and research mathematicians interested in geometry and topology. 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 geometry and topology. Table of Contents  Introduction
 Preliminaries
 Coherent and holonomic \(\mathcal{R}_{\mathcal{X}}\)modules
 Smooth twistor structures
 Specializable \(\mathcal{R}_{\mathcal{X}}\)modules
 Polarizable twistor \(\mathcal {D}\)modules
 Polarizable regular twistor \(\mathcal {D}\)modules on curves
 The decomposition theorem for polarizable regular twistor \(\mathcal {D}\)modules
 Integrability
 Appendix. Monodromy at infinity and partial Fourier Laplace transform
 Bibliography
 Notation
