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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Riemann-Hilbert Correspondence in Dimension 1 In this talk, I will discuss connections on vector bundles and D-modules with regular singularities and then prove the Xnd Hilbert correspondence for connections over curves.
A good introduction to the homological algebra formalism. Akhil Mathew’s Notes on Verdier Duality. My library Help Advanced Book Search. Proofs for most of the results can be found in the following Goresky, Macpherson papers.
MIT Graduate Seminar on D-modules and Perverse Sheaves
Liam marked it as to-read Jun 02, 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.
I will then proceed to set up the sheaf theoretic framework for intersection homology and prove that the IC sheaves thus constructed satisfy conditions on the supports of their stalks that will eventually be used to characterize simple perverse sheaves.
Popular passages Page 11 The book is intended to serve graduate students in a classroom setting and as self-study for researchers in algebraic geometry, and representation theory. This book also contains a good exposition of t-structures. The book is intended to serve graduate students in a classroom setting and as self-study for researchers in algebraic geometry, representation theory.
This paper also has useful background for the decomposition theorem and also provides the earlier proofs of the theorem. Want to Read saving….
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. Jake marked it as to-read Jun 01, These notes have some minor errors which will be fixed soon.
September 22 Siddharth Venkatesh 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.
C2 Functors in derived categories of sheaves. Regular singular holonomic D-modules and the Riemann Hilbert correspondence. Derived Categories and Derived Functors. October 27th Seth Shelley-Abrahamson Riemann-Hilbert Correspondence in Dimension 1 In this talk, I will discuss connections on vector bundles and D-modules with regular singularities and then prove the Riemann Hilbert correspondence for connections over curves.
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 D-modules continues to be an active area of stimulating research in such mathematical areas as algebra, analysis, differential equations, and representation theory. There are no discussion topics on this book yet. This book is not yet featured on Listopia. References more to be added: If you find any major errors, please let me know.
Subsequently, I define the exceptional inverse image of a morphism and the Verdier duality on the derived category of sheaves. The decomposition theorem, perverse sheaves and the topology of algebraic varieties by de Cataldo and Migliorini: Open Preview See a Problem?
Example based introduction to the topological construction of intersection homology. Representations of Lie Algebras and DModules. Theory of Meromorphic Connections.
D-Modules, Perverse Sheaves, and Representation Theory
Hecke Algebras and Hodge Modules. They have a large number of practice problems to help understand computations with perverse representahion. I begin by defining the notion of a t-structure on a triangulated category and then prove that the heart of a t-structure is abelian.
Return to Book Page. Vanishing cycles and nearby cycles: These notes focus on motivating and applying the decomposition theorem.
Matthew Housley marked it as to-read May 26, A5 Smoothness dimensions and local coordinate systems. It has a rather technical treatment, which should be supplemented with something more terse and intuitive, like Bernstein’s lecture notes. To further aid the reader, and to make the work as self-contained as possible, appendices are rspresentation as background for the theory of derived categories and algebraic varieties. Faisceaux Pervers by Beilinson, Bernstein and Deligne: