Buy D-Modules, Perverse Sheaves, and Representation Theory (Progress in Mathematics) on ✓ FREE SHIPPING on qualified orders. Overview. The origin of many authors’ interest in the connection. Representation Theory → Perverse Sheaves lies in the solution of the. Key to D-modules, Perverse Sheaves, and Representation Theory is the authors’ essential algebraic-analytic approach to the theory, which.

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Pavel Etingof and Roman Bezrukavnikov This is a followup to a seminar on D-modules that was held in Springwhich was based on a course taught by Pavel Etingof in Fall I end the talk by exploring the relation of Verdier duality with the other functors and briefly describing the formalism of six functors. This paper also has useful background for the decomposition theorem and also provides the earlier proofs of the theorem. A good introduction to the homological algebra formalism. Goodreads helps you keep track of books you want to read.

Bernstein’s notes on Algebraic D-modules: Open Preview See a Problem?

Theory of Meromorphic Connections. Introduction to Perverse Sheaves In this talk, I introduce the notion of perverse sheaves on stratifiable spaces. Constructible Sheaves on Stratified Spaces In this talk, I reintroduce the notion of a topologically stratified space and look at examples to understand the local topology of a stratified space.

Popular passages Page 11 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 Representatiion correspondence, Hodge modules, and the solution to the Kazhdan-Lusztig conjecture using D-module theory. C3 Noncharacteristic deformation lemma.

## D-Modules, Perverse Sheaves, and Representation Theory

It has d-mldules rather technical treatment, which should be supplemented with something more terse and intuitive, like Bernstein’s lecture notes. I begin by defining perverwe notion of a t-structure on a triangulated category and then prove that the heart of a t-structure is abelian. D -modules continues to be an active area of stimulating research in such mathematical areas as algebraic, analysis, differential equations, and representation theory.

A useful reference for any technical details or proofs of theorems stated in Bernstein’s notes. The original paper on perverse sheaves. If you find any major errors, please let me know.

Hardcoverpages. Key to D-modules, Perverse Sheaves, and Representation Theory is the authors’ essential algebraic-analytic approach to the theory, which Representations of Lie Algebras and DModules. Defining the oerverse of the t-structure as the category of perverse sheaves, I end the talk by giving 5 equivalent definitions of simple perverse sheaves.

This is a followup to a seminar on D-modules that was held in Springwhich was based on a course taught by Pavel Etingof in Fall A5 Smoothness dimensions and local coordinate systems.

## MIT Graduate Seminar on D-modules and Perverse Sheaves (Fall 2015)

Matthew Housley marked it as to-read May 26, Thanks for telling us about the problem. Vanishing cycles and nearby cycles: 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. Character Formula of Highest Weight Modules. B6 Bifunctors in derived categories.

Analytic DModules and the de Rham Functor. I then discuss some of the properties of these functors, namely the adjunction formulas, projection formula, proper base change.

### D-Modules, Perverse Sheaves, and Representation Theory by Ryoshi Hotta

Hecke Algebras and Hodge Modules. Refresh and try again. I will begin by defining the middle perversity intersection complex following Goresky and Macpherson and computing some examples of intersection homology the intersection homology of the affine cone over a smooth projective variety in particular. Xheaves to Book Page. Want to Read Currently Reading Read. The first paper defines the intersection complex using simplicial chains on Repfesentation pseudomanifolds while the second introduces the sheaf theoretic viewpoint following a suggestion of Deligne.

B2 Categories of complexes. Akhil Mathew’s Notes on Verdier Duality. Selected pages Page xi.

Liviu Nicolaescu’s notes on the derived category of sheaves and Pervese Duality: Lists with This Book. E3 Lagrangian subsets of cotangent bundles. E2 Symplectic structures on cotangent bundles. 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.

### MIT Graduate Seminar on D-modules and Perverse Sheaves

Nitin CR added it Mar 25, This book is not yet featured on Listopia. Trivia About D-Modules, Perver No trivia or quizzes yet. Algebraic Groups and Lie Algebras. The decomposition theorem, perverse sheaves and the topology of algebraic varieties by de Cataldo and Migliorini: Books by Ryoshi Hotta. Example based introduction to the topological construction of intersection homology.

Subsequently, I define constructible sheaves on topologically stratified spaces and show an example of how such sheaves correspond to quiver data that describes the fundamental group of shwaves strata and how the different strata are glued together. Derived Categories and Derived Functors.