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Recently in a seminar the following question was raised and, despite my familiarity with theory, I couldn't come up with a good answer: Are there any good reasons to use Tate's theory of rigid-...

$\newcommand{\Sp}{\mathrm{Sp}}\newcommand{\abs}[1]{\lvert #1\rvert}\newcommand{\comptensor}{\mathbin{\hat{\otimes}}}$ Let $k$ be a complete non-archimedian field and let $X = \Sp(B)$ be a $k$-affinoid ...