Daniel Murfet (Australian National University)

Friday 19th October, 12.05-12.55pm, Carslaw 373

Homotopy categories, Grothendieck duality and singularities

It has been understood since the 1980s that there is a deep connection between finiteness conditions on categories of maximal Cohen-Macaulay modules and the character of particular isolated singularities. This can be understood in terms of stable module categories, which are nice examples of triangulated categories. Grothendieck duality describes an important property of another nice triangulated category, the bounded derived category of coherent sheaves on a projective variety. Recent work involving compactly generated homotopy categories has given us new insight into both problems. I will talk about these developments, including results from my PhD thesis.