ROLLING SIMPLEXES AND THEIR COMMENSURABILITY IV. A FAREWELL TO ARMS!

摘要

This text by pure algebraic reasons outlines why the spectrum of maximal ideals Spec_C A of a countable-dimensional differential C-algebra A of transcendence degree 1 without zero divisors is locally analytic, which means that for any C-homomorphism ψ_M: A → C (M ∈ Spec_CA) and any a ∈ A the Taylor series ψ_M(a)=~(def) ∑~∞_(m=0) ψ_M(a~((m)))z~m/m! has nonzero radius of convergence depending on the element a ∈ A.