Berkovich Spaces and Tubular Descent

TL;DR

This paper introduces a novel method for reconstructing coherent sheaves on algebraic varieties using Berkovich spaces, formal neighborhoods, and complements, bridging algebraic and analytic perspectives.

Contribution

It develops a new framework connecting formal neighborhoods, complements, and Berkovich analytic spaces for coherent sheaf construction on algebraic varieties.

Findings

Established a construction method for coherent sheaves using Berkovich spaces.

Defined a new Berkovich analytic space W for sheaf isomorphisms.

Unified algebraic and analytic approaches to sheaf theory on varieties.

Abstract

We consider an algebraic variety X together with the choice of a subvariety Z. We show that any coherent sheaf on X can be constructed out of a coherent sheaf on the formal neighborhood of Z, a coherent sheaf on the complement of Z, and an isomorphism between certain representative images of these two sheaves in the category of coherent sheaves on a Berkovich analytic space W which we define.