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math.NT2026
Abhyankar valuations, Prüfer-Manis valuations, and perfectoid Tate algebras
Dimitri Dine, Jack J Garzella
Let be a perfectoid field. We describe all quotient fields of the perfectoid Tate algebra\begin{equation*}T_{n,K}^{\text{perfd}}=K\langle X_{1}^{1/p^{\infty}},\dots, X_{n}^{1/p…
math.NT2025
Banach modules, almost mathematics and condensed mathematics
Dimitri Dine
We study the relationship between almost mathematics, condensed mathematics and the categories of seminormed and Banach modules over a Banach ring , with submetric (norm-decreas…