Astérisque 2011; 607 pp; softcover Number: 340 ISBN10: 2856293328 ISBN13: 9782856293324 List Price: US$135 Member Price: US$108 Order Code: AST/340
 The author studies (i) the asymptotic behaviour of wild harmonic bundles, (ii) the relation between semisimple meromorphic flat connections and wild harmonic bundles, (iii) the relation between wild harmonic bundles and polarized wild pure twistor \(D\)modules. As an application, he shows the hard Lefschetz theorem for algebraic semisimple holonomic \(D\)modules, conjectured by M. Kashiwara. He also studies resolution of turning points for algebraic meromorphic flat bundles. 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 pure mathematics, analysis, algebra, and algebraic geometry. Table of Contents Part I. Good meromorphic \(\varrho\)flat bundles  Good formal property of a meromorphic \(\varrho\)flat bundle
 Stokes structure of a good \(\varrho\)meromorphic flat bundle
 Full Stokes data and RiemannHilbertBirkhoff correspondence
 \(L^2\)cohomology of filtered \(\lambda\)flat bundle on curves
 Meromorphic variation of twistor structure
Part II. Prolongation of wild harmonic bundle  Prolongments \(\mathcal{PE}^\lambda\) for unramifiedly good wild harmonic bundles
 Some basic results in the curve case
 Associated family of meromorphic \(\lambda\)flat bundles
 Smooth divisor case
 Prolongation and reduction of variations of polarized pure twistor structures
 Prolongation as \(\mathcal{R}\)triple
Part III. KobayashiHitchin correspondence  Preliminaries
 Construction of an initial metric and preliminary correspondence
 Preliminaries for the resolution of turning points
 KobayashiHitchin correspondence and some applications
Part IV. Application to wild pure twistor \(D\)modules  Wild pure twistor \(D\)modules
 The Hard Lefschetz Theorem
 Correspondences
Part V. Appendix  Preliminaries from analysis on multisectors
 Acceptable bundles
 Review on \(\mathcal{R}\)modules, \(\mathcal{R}\)triples and variants
 Bibliography
 Index
