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Usually, Berkovich analytic spaces are derived from some Banach rings (or chains of Banach rings) over a completely normed field $k$ through Berkovich spectrum. But when the base field is the complex ...

Setup. Let $k$ be an algebraically closed field of characteristic zero. Let $X/k$ be a normal variety, and let $Y/k$ be a proper variety. It is well-known that the indeterminacy locus of a rational ...

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 $...

Kodaira embedding theorem can be regarded as a vast generalizaton of the projectivity criterion for complex tori: indeed, the Riemann conditions essentially say that the line bundle defined by the ...

Does every vector bundle on a Stein space have a finite local trivialisation? Definitions: Stein space means either a complex analytic Stein space or a nonarchimedean Stein space in the sense of ...

The "function field analogy" seems to be a topic that is considerably bigger than any one existing writeup conveys. There are several old question on MO and and MathSE that ask for details. One of the ...