All Questions

In his paper Etale cohomology for non-Archimedean analytic space (IHES), Berkovich explained how to glue $k$-analytic spaces (Prop. 1.3.3) and show its uniqueness using the Prop 1.3.2 (gluing morphism)...

Let $K$ be a complete non-archimedean field and let $X$ be a $K$-analytic space in the sense of Berkovich of pure dimension $d$. Let $\varphi \colon X \to \mathbf{G}_m^r$ be a moment map to an ...

Let $k$ be a field and $X$ be a smooth irreducible $k$-variety with an action of a finite group $G$. I consider $k$ as a trivially valued field. It is known from results of Berkovich ("Smooth p-...

Given a non-archimedean field $\mathbb K$, there is a natural map $$ \mathrm{val}: (\mathbb K^*)^n\to\mathbb R^n$$ (See Section 4 of Gubler's paper). Gubler mentions there $\mathrm{val}$ is a ...

This post is closely related to the previous one here. But more generally, we want to study an affinoid algebra $A:=T_n/\mathfrak a$. Let's assume $\mathfrak a= (f_1,\dots,f_r)$ for some $f_i\in T_n$....

It is known that in non-archimedean world there is also a GAGA-functor from the category of $K$-schemes of locally finite type to the category of rigid $K$-spaces. Here $K$ is a field with a non-...