000			03082 a2200325 4500
003			NISER
005			20260121173509.0
008			260121b |||||||| |||| 00| 0 hin d
020			_a9781470455972 _qPaperback
040			_aNISER LIBRARY _beng _cNISER LIBRARY
082	0	4	_a512.54 _bACH-P
100	1		_aAchar, Pramod N.
245	1	0	_aPerverse sheaves and applications to representation theory
260			_aProvidence, Rhode Island : _bAmerican Mathematical Society, _c2021.
300			_axii, 562 pages : _billustrations ; _c26 cm.
490			_aMathematical surveys and monographs, _vvolume 258 _x0076-5376 ;
504			_aIncludes bibliographical references (pages 545-556) and index.
520			_aSince 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 compre hensive 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 equi variant derived category, and brief surveys of side topics including étale and -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 calcula tions 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.
650		0	_aSheaf theory
650		0	_aRepresentations of groups
650		0	_aLinear algebraic groups
650		7	_aSeveral complex variables and analytic spaces _xComplex singularities _xStratifications; constructible sheaves; intersection cohomology (complex-analytic aspects)
650		7	_aGroup theory and generalizations -- Linear algebraic groups and related topics -- Representation theory for linear algebraic groups
650		7	_aAlgebraic geometry -- Special varieties -- Grassmannians, Schubert varieties, flag manifolds
650		7	_aNonassociative rings and algebras -- Lie algebras and Lie superalgebras -- Coadjoint orbits; nilpotent varieties
650		7	_aNonassociative rings and algebras -- Lie algebras and Lie superalgebras -- Quantum groups (quantized enveloping algebras) and related deformations
856	4	1	_3Table of contents _uhttps://www.ams.org/books/surv/258/surv258-endmatter.pdf
856	4	1	_3Reviews _uhttps://www.goodreads.com/book/show/65647054-perverse-sheaves-and-applications-to-representation-theory?ref=nav_sb_ss_1_13#CommunityReviews
942			_cBK _2udc
999			_c36532 _d36532