Relating two genus 0 problems of John Thompson

Details Relating two genus 0 problems of John Thompson Relating two genus 0 problems of John Thompson

2009-10-20

arxiv.org/abs/0910.3974v1

Volume for John Thompson's 70th birthday, in Progress in Galois Theory, H. Voelklein and T. Shaska editors 2005 Springer Scien

Mathematics

Algebraic Geometry

Scientific paper

The "relating" entwines three problems: 1. Davenport's Problem, describing pairs of polynomials over Q whose ranges on Z/p are the same for almost all p. 2. Showing that the monodromy groups of rational function maps over the complexes are limited to a finite set of groups, outside of groups close to alternating groups (example, symmetric groups) with special representations, and dihedral and cyclic groups. 3. Relating the genus 0 modular curves to the character group of the Monster simple group, so-called Monstrous Moonshine. http://www.math.uci.edu/~mfried/pathlist-cov/thomp-genus0.html has a more detailed exposition on the paper; http://www.math.uci.edu/~mfried/deflist-cov/Genus0-Prob.html gives a separate description of genus 0 problem #2.

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