 
Summary: Applications of Homological Algebra Introduction to Perverse Sheaves
Spring 2007 P. Achar
Problem Set 8
March 20, 2007
The goal of this problem set is to illustrate that the concept of tstructure is not trivial: the heart of a
nontrivial tstructure on the derived category of an abelian category need not be equivalent to the original
abelian category.
NOTE: Please do not hand in Problem 1 for credit. (You may of course hand it in if you just want me to
look over your solution.)
1. Let A (resp. B) be the category whose objects V are diagrams of complex vector spaces of the form
V1 V2 V3 resp. V1 V2 V3,
and in which a morphism f : V W is a commutative diagram
V1
//
f1
V2
f2
V3
