Compactly generated homotopy categories and Grothendieck duality

Daniel Murfet – 24 October 2007

It has been known for some time that there is a deep connection between stable module categories of maximal Cohen-Macaulay modules and properties of singularities on algebraic varieties. Recent work involving compactly generated homotopy categories has highlighted some connections between these stable module categories and bounded derived categories of coherent sheaves, which are another class of interesting triangulated categories. I will talk about these developments, including results from my PhD thesis.