Applications of Homological Algebra: Introduction to Perverse Sheaves
Spring 2007

Class: Tues. & Thurs. 10:40am–12:00pm in 113 Lockett Hall
Office hours: Tues. 2:00pm–3:30pm or by appointment
Quick Reference Guide
Problem Sets

Jan. 18: PS 1
Jan. 30: PS 2
Feb. 1: PS 3
Feb. 8: PS 4
Feb. 15: PS 5
Mar. 1: PS 6
Mar. 13: PS 7
Mar. 20: PS 8
Mar. 22: PS 9
Mar. 29: PS 10
Apr. 12: PS 11
Apr. 26: PS 12

Basic Facts on Sheaves
Operations on Sheaves; Adjointness Theorems
Local Systems and Constructible Sheaves
Categories of Complexes; Distinguished Triangles
Derived Categories and Derived Functors
Derived Functors in Categories of Sheaves
Proper Pull-Back and Poincaré–Verdier Duality
Triangulated Categories and t-Structures
Gluing t-Structures; Perverse Sheaves
Goresky–MacPherson Stratifications and Perversities

  1. M. Kashiwara and P. Schapira, Sheaves on Manifolds, Grundlehren der Mathematischen Wissenschaften, Springer-Verlag, 1990.
    The first two chapters of this book give an excellent account of derived categories in general and of sheaves on a topological space, but most of the rest of the book is beyond the scope of this course.
  2. A. Beilinson, J. Bernstein, and P. Deligne, Faisceaux pervers, in Analyse et topologie sur les espaces singuliers I (Luminy, 1981), Astérisque 100 (1982).
    This is the monograph in which the theory of perverse sheaves was first developed.  It's somewhat dense, but it's still the best reference for all the relevant material.
  3. R. Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, 1977.
    §II.1 of this book is a good brief account of the basics of sheaves.