Math 7260
Homological Algebra
Fall 2015
P. Achar
Problem Set 2
Due: September 29, 2015
1. Let R = C[t]/(t2 ), and let N = R/(t). Show that Exti (N, N )
= C for all i 0.
2. Weibel, Exercise 2.3.5.
3. Weibel, Exercise 2.3.7.
4. Weibel, Exercise 2.4.4. (Jus

Math 7260
Homological Algebra
Fall 2015
P. Achar
Problem Set 1
Due: September 10, 2015
1. (Do not hand in) Weibel, Exercises 1.1.1, 1.1.2, 1.1.5.
2. (Do not hand in) Show that any isomorphism of chain complexes is a quasi-isomorphism.
3. (Do not hand in)

Math 7260
Homological Algebra
Fall 2015
P. Achar
Problem Set 3
Due: November 3, 2015
1. Let A be an abelian category with enough projectives, and let A A. Regard A as a chain complex
concentrated in degree 0. Choose a projective resolution P A. (Recall th

Math 7260
Homological Algebra
Fall 2015
P. Achar
Problem Set 4
Due: December 7, 2015
1. (Not to hand in) Let R = C[t, t1 ], the ring of Laurent polynomials in one variable. An R-module is
the same as a complex vector space V equipped with an automorphism

Math 7260
Homological Algebra
Spring 2014
P. Achar
Derived Categories Cheat Sheet
1. A triangulated category is an additive category T equipped with an automorphism (called shift or
translation) [1] : T T and a collection of diagrams (called distinguished

Math 7260
Homological Algebra
Spring 2014
P. Achar
Problem Set 5 (Optional)
Due: May 6, 2014
1. Use a spectral sequence argument to do Problem 5 on Problem Set 4.
2. Let X be a fixed abelian group, and let F : Z-mod Z-mod be the functor F (M ) = Tor1 (X,

Math 7260
Homological Algebra
Spring 2014
P. Achar
Course Information
Office:
Phone:
E-mail:
Webpage:
266 Lockett Hall
578-7990
pramod@math.lsu.edu
http:/www.math.lsu.edu/~pramod/
Textbook. For most of the semester, we will work from the following book: