3 papers
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.AC2025
On Shilov boundaries, Rees valuations and integral extensions
Dimitri Dine
We explore an analogy between, on one hand, the notions of integral closure of ideals and Rees valuations in commutative algebra and, on the other hand, the notions of spectral sem…
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…