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A Geometric characterization of Arithmetic Varieties

Kapil Hari Paranjape
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Abstract

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.

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Kapil Hari Paranjape. 2002-04-08. A Geometric characterization of Arithmetic Varieties. https://arxiv.org/abs/math/0111091

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