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Belyi’s theorem states that a smooth projective complex algebraic curve (i.e. a compact Riemann surface) can be defined over a number field if and only if it can be expressed as a branched covering of the projective line ramified over at most 3 points, providing a purely topological characterization of an arithmetic condition. I will present a proof of this result and sketch how it leads to Grothendieck’s theory of dessin d'enfants.

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