nLab strict analytic geometry

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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)||g(x)|0}\{x,\;|f(x)|\leq |g(x)|\neq 0\}) in polydiscs of radius one.

In the pp-adic setting, strict analytic geometry is usually called rigid analytic geometry. In the archimedean setting (i.e., over C\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 14:30:55. See the history of this page for a list of all contributions to it.