  A result of Belyi can be stated as follows. Every curve defined over a number
field can be expressed as a cover of the projective line with branch locus
contained in a rigid divisor. We define the notion of geometrically rigid
divisors in surfaces and then show that every surface defined over a number
field can be expressed as a cover of the projective plane with branch locus
contained in a geometrically rigid divisor in the plane. The main result is the
characterisation of arithmetically defined divisors in the plane as
geometrically rigid divisors in the plane.

Algebraic Geometry;Number Theory