On local properties of non-Archimedean analytic spaces II

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Relative p-adic Hodge theory, II: Imperfect period rings (2016, methodology): “Following Temkin [121], we define the associated graded ring GrA = ⊕”
Stable modification of relative curves (2007, background): “It is proven in [ Tem2 ], 2.1, that the sets RZ K (A) are quasi-compact (it is assumed in the formulation, that A contains a field k, but this assumption is not used in the proof).”
Several approaches to non-archimedean geometry (2008, background): “Prove that this is a bounded multiplicative seminorm on A . Also show that it deserves to be called the sup-norm on the closed disc of radius r (with center at 0) in the sense that||f||r is the supremum of the numbers |f|x as|·|x ranges through all bounded k-algebra maps A ! K to nonarchimedean fiel”