A geometric characterization of arithmetic varieties
Click here to view fulltext PDF
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 characterization of arithmetically defined divisors in the plane as geometrically rigid divisors in the plane.
Volume 133, 2023
Continuous Article Publishing mode
Click here for Editorial Note on CAP Mode