nLab strict analytic geometry

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.

Related concepts

• rigid analytic geometry
• overconvergent global analytic geometry