Mathematical Research Letters
Volume 22 (2015)
Exceptional collections on 2-adically uniformized fake projective planes
Pages: 43 – 57
We show that there exist exceptional collections of length $3$ consisting of line bundles on the three fake projective planes that have a $2$-adic uniformization with torsion-free covering group. We also compute the Hochschild cohomology of the right orthogonal of the subcategory of the bounded derived category of coherent sheaves generated by these exceptional collections.