Berkovich Spaces and Tubular Descent

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.

20 pages

References in corpus (1)

• Moduli Stacks of Bundles on Local Surfaces

Cited by in corpus (9)

• Non-Archimedean analytic geometry as relative algebraic geometry
• Refinements to patching and applications to field invariants
• Normalized Berkovich spaces and surface singularities
• Moduli Stacks of Bundles on Local Surfaces
• Fréchet Modules and Descent
• Milnor descent for cohesive dg-categories
• Categorical Logarithmic Hodge Theory, I
• Adelic Descent Theory
• Descent via Tannaka duality