Derived categories of Keum's fake projective planes

Sergey Galkin, Ludmil Katzarkov, Anton Mellit, Evgeny Shinder

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)238-253
Number of pages16
JournalAdvances in Mathematics
StatePublished - Jun 5 2015
Externally publishedYes


  • Derived categories of coherent sheaves
  • Exceptional collections
  • Fake projective planes

ASJC Scopus subject areas

  • Mathematics(all)


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