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Article

Derived categories of Keum's fake projective planes

Advances in Mathematics. 2015. Vol. 278. P. 238-253.
Galkin S., Katzarkov L., Mellit A., Shinder E.

We conjecture that derived categories of coherent sheaves on fake projective n-spaces have a semi-orthogonal decomposition into a collection of n+1 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.