Derived categories of coherent sheaves

  • Tom Bridgeland

    University of Sheffield, United Kingdom
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We discuss derived categories of coherent sheaves on algebraic varieties. We focus on the case of non-singular Calabi–Yau varieties and consider two unsolved problems: proving that birational varieties have equivalent derived categories, and computing the group of derived autoequivalences. We also introduce the space of stability conditions on a triangulated category and explain its relevance to these two problems.