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In the end of Section 9.2 of Bosch's book Lectures on Formal and Rigid Geometry, a rigid $S$-space $E_Q$ is constructed, for a variable $Q$ replacing the classical parameter $q\in k$. (Here $k$ is a non-archimedean field and $S=\mathrm{Spf}\mathbb Z[[Q]]$). Then $E_Q$ may be viewed as the family of all Tate elliptic curves by looking at the morphism $Z[[Q]] \to k^\circ, Q\mapsto q$.

(1) It looks interesting but the reference is missing in Bosch's book. Which one of Raynaud's paper is about this construction?

(2) Could we in some sense further generalize it by considering more than one variables, i.e. $S'=\mathbb Z[[Q_1,\dots, Q_k]]$? Notice that $S'$ seems still satisfy the condition $(N)$ required by Bosch (see p 162)

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Q1: Michel Reynaud, Géométrie analytique rigide d’après Tate, Kiehl..., Bull. Soc. Math. France, Mémoire 39-40, p. 319-327 (1974).

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