D-Modules, Perverse Sheaves, and Representation Theory
D-Modules, Perverse Sheaves, and Representation Theory by Ryoshi Hotta, published by Springer Science & Business Media in 2007, offers a comprehensive exploration of D-modules and their applications in various mathematical fields. This edition, consisting of 412 pages, presents an algebraic-analytic approach that connects D-modules to representation theory, along with significant concepts such as holonomic D-modules, perverse sheaves, and the Riemann-Hilbert correspondence.
Readers will find a detailed examination of essential topics that have emerged in recent decades, including Hodge modules and the Kazhdan-Lusztig conjecture. The book also includes appendices designed to provide background on derived categories and algebraic varieties, making it suitable for graduate students and researchers in algebraic geometry and representation theory. This work aims to be both a classroom resource and a self-study guide, facilitating a deeper understanding of the intricate relationships within these mathematical domains.
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D-modules continues to be an active area of stimulating research in such mathematical areas as algebra, analysis, differential equations, and representation theory.
Key to D-modules, Perverse Sheaves, and Representation Theory is the authors’ essential algebraic-analytic approach to the theory, which connects D-modules to representation theory and other areas of mathematics. Significant concepts and topics that have emerged over the last few decades are presented, including a treatment of the theory of holonomic D-modules, perverse sheaves, the all-important Riemann-Hilbert correspondence, Hodge modules, and the solution to the Kazhdan-Lusztig conjecture using D-module theory.
To further aid the reader, and to make the work as self-contained as possible, appendices are provided as background for the theory of derived categories and algebraic varieties. The book is intended to serve graduate students in a classroom setting and as self-study for researchers in algebraic geometry, and representation theory.
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