The representability hierarchy and Hilbert’s 13th problem
نویسندگان
چکیده
We propose the representability hierarchy of algebraic functions over C, which relates classic questions like the unsolvability of the quintic by radicals to unresolved questions like Hilbert’s 13th problem in its original algebraic form. We construct the theory of algebraic functions via both superpositions and algebraic geometry and then justify the known positions of the universal algebraic functions ρn in the hierarchy. Relationships to algebraic topology, Galois theory, birational geometry, and prior literature on representability are also discussed.
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