Unifying themes suggested by Belyi’s Theorem

Wushi Goldring ()
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Wushi Goldring: Harvard University, Department of Mathematics

A chapter in Number Theory, Analysis and Geometry, 2012, pp 181-214 from Springer

Abstract: Abstract Belyi’s Theorem states that every curve defined over the field of algebraic numbers admits a map to the projective line with at most three branch points. This paper describes a unifying framework, reaching across several different areas of mathematics, inside which Belyi’s Theorem can be understood. The paper explains connections between Belyi’s Theorem and (1) The arithmetic and modularity of elliptic curves, (2) abc-type problems and (3) moduli spaces of pointed curves.

Keywords: Belyi’s Theorem; abc; moduli of curves (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-1260-1_10

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DOI: 10.1007/978-1-4614-1260-1_10

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