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rigid analytic varieties, affinoid varieties, strictly convergent power series over non-archimedean fields

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Projective reduction of image of power series is algebraic?

Let $K$ be a non-archimedean field with closed unit disk $\mathcal{O}\subset K$, open unit disk $\mathfrak{m}\subset \mathcal{O}$ and residue field $k = \mathcal{O}/\mathfrak{m}$. Examples to keep in …