Derived Morita theory for Grothendieck categories

Jorge Vitória (Verona)

Frank Adams 1,

Rickard's derived Morita theorem states that rings derived equivalent to a fixed one can be parametrised by compact tilting complexes. In this talk we discuss how to generalise this result to Grothendieck abelian categories. We show that two Grothendieck abelian categories are derived equivalent if and only if they are related by a cotilting complex. Moreover, we prove that, given a Grothendieck category whose derived category is compactly generated (such as derived categories of rings or derived categories of quasi-coherent sheaves over quasi-compact separated schemes), all derived equivalent Grothendieck categories can be obtained from pure-injective cotilting complexes. This is joint work with Chrysostomos Psaroudakis and ongoing joint work with Lidia Angeleri Hügel and Frederik Marks.

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