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Arithmetic structure of CMSZ fake projective planes

Fumiharu Kato·Hiroyuki Ochiai
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Abstract

We prove that the fake projective planes constructed from the diadic discrete group discovered by Cartwright, Mantero, Steger, and Zappa are connected Shimura varieties associated to a certain unitary group. The necessary Shimura data, as well as the unitary group, are explicitly described. We also give a field of definition of these fake projective planes.

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Fumiharu Kato, Hiroyuki Ochiai. 2000-06-29. Arithmetic structure of CMSZ fake projective planes. https://arxiv.org/abs/math/0006223

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