# nLab strict analytic geometry

### Context

#### Analytic geometry

analytic geometry (complex, rigid, global)

## Basic concepts

analytic function

analytification

GAGA

# Contents

## Idea

Strict analytic geometry is the study of analytic spaces over Banach rings with building blocs given by strict rational domains (defined, for example, by relations of the form $\{x,\;|f(x)|\leq |g(x)|\neq 0\}$) in polydiscs of radius one.

In the $p$-adic setting, strict analytic geometry is usually called rigid analytic geometry. In the archimedean setting (i.e., over $\C$), strict analytic geometry is essentially equivalent to usual analytic geometry.

There is a natural notion of strict global analytic geometry that has some non-trivial relation with the ideas of Arakelov geometry.