Rolling Simplexes and Their Commensurability IV. A Farewell to Arms!*

Abstract

This text by pure algebraic reasons outlines why the spectrum of maximal ideals Spec_ℂA 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 \( {\overset{\sim }{\psi}}_M(a)\overset{\mathrm{def}}{=}\sum \limits_{m=0}^{\infty }{\psi}_M\left({a}^{(m)}\right)\frac{z^m}{m!} \) has nonzero radius of convergence depending on the element a ∈ A.