Injective resolutions for unbounded chain complexes

Jérome Scherer – 22 October 2008

This is joint work in progress with W. Chacholski and W. Pitsch. I will explain three approaches to the problem of constructing injective resolutions for unbounded complexes, by Spaltenstein, Bökstedt and Neeman, and ours. I will then talk about relative homological algebra in this setting, discuss how this can arise by restricting the number of injective objects one is ready to consider. I will finally present an example due to A. Neeman which shows that the construction of resolutions in the relative setting can be complicated.