Softcover ISBN:  9781470455972 
Product Code:  SURV/258 
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eBook ISBN:  9781470466688 
Product Code:  SURV/258.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9781470455972 
eBook: ISBN:  9781470466688 
Product Code:  SURV/258.B 
List Price:  $250.00$187.50 
MAA Member Price:  $225.00$168.75 
AMS Member Price:  $200.00$150.00 
Softcover ISBN:  9781470455972 
Product Code:  SURV/258 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9781470466688 
Product Code:  SURV/258.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9781470455972 
eBook ISBN:  9781470466688 
Product Code:  SURV/258.B 
List Price:  $250.00$187.50 
MAA Member Price:  $225.00$168.75 
AMS Member Price:  $200.00$150.00 

Book DetailsMathematical Surveys and MonographsVolume: 258; 2021; 562 ppMSC: Primary 32; 14; 20; 17;
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 \(\ell\)adic sheaves, \(\mathcal{D}\)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: KazhdanLusztig 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 4page “Quick Reference” that summarizes the most commonly used facts for computations, similar to a table of integrals in a calculus textbook.ReadershipGraduate students and researchers interested in representation theory, derived categories, and perverse sheaves.

Table of Contents

Chapters

Sheaf theory

Constructible sheaves on complex algebraic varieties

Perverse sheaves

Nearby and vanishing cycles

Mixed sheaves

Equivariant derived categories

KazhdanLusztig theory

Springer theory

The geometric Satake equivalence

Quiver representations and quantum groups

Category theory and homological algebra

Calculations on $\mathbb {C}^n$

Quick reference


Additional Material

Reviews

...Pramod Achar provides a very nice and comprehensive introduction to the theory of perverse sheaves with an emphasis on their applications to representation theory.
...In the author's opinion, perverse sheaves are easy, in the sense that most arguments come down to a rather short list of tools, such as proper base change, smooth pullback, and openclosed distinguished triangles. The author tries to emphasize this perspective with computational exercises and with the Quick Reference. This is the main feature of this book. I believe this book is a valuable reference for algebraists who want to learn the theory of perverse sheaves. Readers can profit tremendously from attempting the hundreds of exercises scattered throughout the book.
Jun Hu, Beijing Institute of Technology


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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 \(\ell\)adic sheaves, \(\mathcal{D}\)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: KazhdanLusztig 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 4page “Quick Reference” that summarizes the most commonly used facts for computations, similar to a table of integrals in a calculus textbook.
Graduate students and researchers interested in representation theory, derived categories, and perverse sheaves.

Chapters

Sheaf theory

Constructible sheaves on complex algebraic varieties

Perverse sheaves

Nearby and vanishing cycles

Mixed sheaves

Equivariant derived categories

KazhdanLusztig theory

Springer theory

The geometric Satake equivalence

Quiver representations and quantum groups

Category theory and homological algebra

Calculations on $\mathbb {C}^n$

Quick reference

...Pramod Achar provides a very nice and comprehensive introduction to the theory of perverse sheaves with an emphasis on their applications to representation theory.
...In the author's opinion, perverse sheaves are easy, in the sense that most arguments come down to a rather short list of tools, such as proper base change, smooth pullback, and openclosed distinguished triangles. The author tries to emphasize this perspective with computational exercises and with the Quick Reference. This is the main feature of this book. I believe this book is a valuable reference for algebraists who want to learn the theory of perverse sheaves. Readers can profit tremendously from attempting the hundreds of exercises scattered throughout the book.
Jun Hu, Beijing Institute of Technology