nLab strict analytic geometry

Contents

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.

Last revised on July 8, 2015 at 10:30:55. See the history of this page for a list of all contributions to it.