Non-archimedean pinchings

TL;DR

This paper develops the theory of pinchings in non-archimedean analytic spaces, demonstrating that while pinchings of affinoid spaces may not be affinoid, pinchings of Hausdorff spaces always exist within the analytic space category.

Contribution

It introduces the concept of pinchings in non-archimedean analytic geometry and proves existence results for pinchings of Hausdorff spaces.

Findings

Pinchings of affinoid spaces may not be affinoid.

Pinchings of Hausdorff spaces always exist in the analytic category.

The theory extends non-archimedean analytic space manipulations.

Abstract

We develop the theory of pinchings for non-archimedean analytic spaces. In particular, we show that although pinchings of affinoid spaces do not have to be affinoid, pinchings of Hausdorff analytic spaces always exist in the category of analytic spaces.