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Polarizable Twistor $$\mathcal D$$-modules
Claude Sabbah, Ecole Polytechnique, Palaiseau, France
A publication of the Société Mathématique de France.
 Astérisque 2005; 208 pp; softcover Number: 300 ISBN-10: 2-85629-174-0 ISBN-13: 978-2-85629-174-0 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