My goal in this class is to cover the folloiwng topics.
Homological algebra arose from problems in geometry, but the first several topics are purely algebraic. On the other hand, derived categories have been an important tool in geometry since they were invented by Grothendieck. In the last several years, they have become even more important as there has been a great deal of interest in the derived category of coherent sheaves on algebraic varieites. I hope to touch on this at the end of the class by lecturing on Beilinson's paper on the derived category of coherent sheaves on complex projective n-space.
I plan to assing several short homework assignments, mostly problems from the text. They will be graded in an appropriate way for a graduate class, that is, leniently. I will post assignments on the Canvas page for our class. However, as some people do not have access to Canvas yet, I will post the first few here.
When people ask me about a problem, I will put the solutions on canvas. For example, I have done this for problem A.1.3 in Weibel, the problem on Pontryagin duality.