2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62593A 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.8 Pages, AMSLaTeXAlgebraic GeometryNumber Theory14J20; 11G35; 51A25text