All Questions

It may seem silly to ask "Why are there three types of non-Archimedean geometry?", that would be like asking why there are three (and even more) different Weil cohomologies. So I have to ...

I have a question related to the definition of the etale site of an adic space. As a reference, I am using Huber's book "Etale Cohomology of Rigid Analytic Varieties and Adic Spaces". First ...

I have heard that there exist examples of Huber pairs $(A,A^{\circ})$ and $(B,B^+)$ such that $\operatorname{Spa}(B,B^+)$ is a rational open of $\operatorname{Spa}(A,A^{\circ})$ and such that $B^+ \...

In his 2012 CDM proceedings, Peter Scholze mentions the following open question: Let $K$ be a perfectoid field and $(A,A^+)$ a complete affinoid $K$-algebra. Suppose there exists a cover of $X = \...

I am reading the Scholze-Weinstein Berkeley lecture notes on "Perfectoid Spaces", and in particular I am stuck trying to understand the closed adic unit disk, which is the second example of ...

I am currently reading the Berkeley lectures on Perfectoid Spaces by Scholze and Weinstein. In the section "The adic open unit disk over $\mathbb{Z}_p$" we encounter from Proposition 4.2.6 ...