A quasi-phantom category is an admissible category in the bounded derived category of a smooth projective variety having trivial Hochschild homology and finite Grothendieck group. If, in addition,
the Grothendieck group vanishes, then we call such a category a phantom. In these talks I will first give an introduction to derived categories, semiorthogonal decompositions etc., before explaining how the first example of a quasi-phantom category, namely in the bounded derived category of the classical Godeaux surface, was constructed. To conclude I will describe some of the subsequent developments and discuss possible questions.
Seminar
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