Geodesic
Rolling simplexes and their commensurability. IV. (A farewell to arms!)
Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 2, pp. 145-156 
O. V. Gerasimova; Yu. P. Razmyslov. Rolling simplexes and their commensurability. IV. (A farewell to arms!). Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 2, pp. 145-156. http://geodesic.mathdoc.fr/item/FPM_2016_21_2_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The text by pure algebraic reasons outlines why the spectrum of maximal ideals $\mathrm{Spec}_\mathbb{C} A$ of a countable-dimensional differential $\mathbb{C}$-algebra $A$ of transcendence degree $1$ without zero divisors is locally analytic, which means that for any $\mathbb{C}$-homomorphism $\psi_M \colon A \to \mathbb{C}$ ($M \in \mathrm{Spec}_{\mathbb C} A$) and any $a \in A$ the Taylor series $\tilde{\psi}_M (a) ={}$ $\sum\limits_{m=0}^{\infty} \psi_M(a^{(m)}) \frac{z^m}{m!}$ has nonzero radius of convergence depending on the element $a \in A$.

[1] Gerasimova O. V., Pogudin G. A., Razmyslov Yu. P., “Rolling simplexes and their commensurability. III (sootnosheniya Kapelli i ikh primeneniya v differentsialnykh algebrakh)”, Fundament. i prikl. matem., 19:6 (2014), 7–24 | MR

[2] Shafarevich I. R., Osnovy algebraicheskoi geometrii, MTsNMO, M., 2007 | MR