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Let $K$ be a non-archimedean field with valuation ring $(V,\mathfrak{m})$, and $K\langle t_1,\ldots, t_n\rangle$ a Tate algebra of convergent power series. Fix $f \in V\langle t_1,\ldots, t_n\rangle$....

The specialization map $sp:\mathfrak{X}_\eta\to \mathfrak{X}_{red}$ has an important role in rigid analytic geometry. I tried looking in Huber's papers ("Continuous Valuations", "A generalization of ...