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suppose $X$ is a proper and smooth rigid analytic variety over $\text{Spa}(k)$, with $k$ a non-archimedean field of characteristic zero. One has the de Rham complex of analytic differential forms on $...

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 ...

In Lemma 7.1.6 of his lecture notes on perfectoid spaces, Bhatt states that every complete characteristic p perfect Tate ring $A$ is uniform. In the proof he uses the Banach open mapping theorem on ...

Are there a polynomials $f_1,...f_n \in \mathbb{Z}_p[x_1,...x_n]$ with there coeficients $p$-adic integers s.t. A map $F:\mathbb{Z}_p^n\rightarrow \mathbb{Z}_p^n$ defined by $f_1,...f_n$ satisfy the ...

Suppose $K$ is a number field, and $A\in M_n(K)$. $v$ is a place of $K$, and $f_1,\cdots,f_n$ are analytic functions (one variable) on $m_v\mathcal O_{K,v}$, satisfying: $\frac{\mathrm d \bf {f}}{\...