Variables Separated Equations and Finite Simple Groups
نویسنده
چکیده
[UMSt] www.math.uci.edu/ ̃mfried/paplist-cov/UMStory.html. Algebraic equations in separated variables: (*) f(x)−g(y) = 0. Defines a projective nonsingular algebraic curve Xf,g with two projections to the (Riemann sphere) z-line Pz = C ∪ {∞}: f : Px → Pz and g : Py → Pz. Two problems from the 60s (Davenport’s and Shinzel’s) solved by the monodromy method . I explain that and the associated Genus 0 Problem. Another genus 0 problem, related to John Thompson, connects the Monster simple group to genus 0 modular curves. Both influenced by the same conference – Santa Cruz (proceedings in 1980).
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