Perverse Sheaves and Applications to Representation Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Perverse Sheaves and Applications to Representation Theory write by Pramod N. Achar. This book was released on 2021-09-27. Perverse Sheaves and Applications to Representation Theory available in PDF, EPUB and Kindle. Since its inception around 1980, the theory of perverse sheaves has been a vital tool of fundamental importance in geometric representation theory. This book, which aims to make this theory accessible to students and researchers, is divided into two parts. The first six chapters give a comprehensive account of constructible and perverse sheaves on complex algebraic varieties, including such topics as Artin's vanishing theorem, smooth descent, and the nearby cycles functor. This part of the book also has a chapter on the equivariant derived category, and brief surveys of side topics including étale and ℓ-adic sheaves, D-modules, and algebraic stacks. The last four chapters of the book show how to put this machinery to work in the context of selected topics in geometric representation theory: Kazhdan-Lusztig theory; Springer theory; the geometric Satake equivalence; and canonical bases for quantum groups. Recent developments such as the p-canonical basis are also discussed. The book has more than 250 exercises, many of which focus on explicit calculations with concrete examples. It also features a 4-page “Quick Reference” that summarizes the most commonly used facts for computations, similar to a table of integrals in a calculus textbook.
D-Modules, Perverse Sheaves, and Representation Theory
D-Modules, Perverse Sheaves, and Representation Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook D-Modules, Perverse Sheaves, and Representation Theory write by Ryoshi Hotta. This book was released on 2007-11-07. D-Modules, Perverse Sheaves, and Representation Theory available in PDF, EPUB and Kindle. D-modules continues to be an active area of stimulating research in such mathematical areas as algebraic, 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. 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, representation theory.
Intersection Homology & Perverse Sheaves
Intersection Homology & Perverse Sheaves - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Intersection Homology & Perverse Sheaves write by Laurenţiu G. Maxim. This book was released on 2019-11-30. Intersection Homology & Perverse Sheaves available in PDF, EPUB and Kindle. This textbook provides a gentle introduction to intersection homology and perverse sheaves, where concrete examples and geometric applications motivate concepts throughout. By giving a taste of the main ideas in the field, the author welcomes new readers to this exciting area at the crossroads of topology, algebraic geometry, analysis, and differential equations. Those looking to delve further into the abstract theory will find ample references to facilitate navigation of both classic and recent literature. Beginning with an introduction to intersection homology from a geometric and topological viewpoint, the text goes on to develop the sheaf-theoretical perspective. Then algebraic geometry comes to the fore: a brief discussion of constructibility opens onto an in-depth exploration of perverse sheaves. Highlights from the following chapters include a detailed account of the proof of the Beilinson–Bernstein–Deligne–Gabber (BBDG) decomposition theorem, applications of perverse sheaves to hypersurface singularities, and a discussion of Hodge-theoretic aspects of intersection homology via Saito’s deep theory of mixed Hodge modules. An epilogue offers a succinct summary of the literature surrounding some recent applications. Intersection Homology & Perverse Sheaves is suitable for graduate students with a basic background in topology and algebraic geometry. By building context and familiarity with examples, the text offers an ideal starting point for those entering the field. This classroom-tested approach opens the door to further study and to current research.
Weil Conjectures, Perverse Sheaves and l-adic Fourier Transform
Weil Conjectures, Perverse Sheaves and l-adic Fourier Transform - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Weil Conjectures, Perverse Sheaves and l-adic Fourier Transform write by Reinhardt Kiehl. This book was released on 2013-03-14. Weil Conjectures, Perverse Sheaves and l-adic Fourier Transform available in PDF, EPUB and Kindle. The authors describe the important generalization of the original Weil conjectures, as given by P. Deligne in his fundamental paper "La conjecture de Weil II". The authors follow the important and beautiful methods of Laumon and Brylinski which lead to a simplification of Deligne's theory. Deligne's work is closely related to the sheaf theoretic theory of perverse sheaves. In this framework Deligne's results on global weights and his notion of purity of complexes obtain a satisfactory and final form. Therefore the authors include the complete theory of middle perverse sheaves. In this part, the l-adic Fourier transform is introduced as a technique providing natural and simple proofs. To round things off, there are three chapters with significant applications of these theories.
Sheaves in Topology
Sheaves in Topology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Sheaves in Topology write by Alexandru Dimca. This book was released on 2012-12-06. Sheaves in Topology available in PDF, EPUB and Kindle. Constructible and perverse sheaves are the algebraic counterpart of the decomposition of a singular space into smooth manifolds. This introduction to the subject can be regarded as a textbook on modern algebraic topology, treating the cohomology of spaces with sheaf (as opposed to constant) coefficients. The author helps readers progress quickly from the basic theory to current research questions, thoroughly supported along the way by examples and exercises.
