Derived categories of Keum's fake projective planes


We conjecture that derived categories of coherent sheaves on fake projective $n$-spaces have a semi-orthogonal decomposition into a collection of exceptional objects and a category with vanishing Hochschild homology. We prove this for fake projective planes with non-abelian automorphism group (such as Keum’s surface). Then by passing to equivariant categories we construct new examples of phantom categories with both Hochschild homology and Grothendieck group vanishing.

Adv. Math. 278 (2015), 238–253