Descent for coherent sheaves along formal/open coverings

TL;DR

This paper proves that coherent sheaves on a regular noetherian scheme with a normal crossings divisor satisfy descent with respect to a covering formed by open parts of completions along divisor components and their intersections.

Contribution

It establishes descent properties of coherent sheaves for a specific covering related to divisors with normal crossings, extending previous understanding in algebraic geometry.

Findings

Coherent sheaves satisfy descent along the specified coverings.

The result applies to schemes with divisors having strict normal crossings.

Provides a new tool for studying sheaves in the context of formal and open coverings.

Abstract

For a regular noetherian scheme $X$ with a divisor with strict normal crossings $D$ we prove that coherent sheaves satisfy descent w.r.t. the 'covering' consisting of the open parts in the various completions of $X$ along the components of $D$ and their intersections.