Morphing etale spaces

TL;DR

This paper provides a straightforward description of sheaves on the small etale site of certain schemes, enabling a clear characterization of which sheaves are representable.

Contribution

It offers a new simple description of sheaves on the small etale site for schemes with specific local properties, enhancing understanding of their structure.

Findings

Characterization of sheaves on the small etale site.

Identification of conditions for representable sheaves.

Simplification of the category description.

Abstract

We give a simple description of the category of sheaves on the small etale site of an irreducible scheme whose local rings are geometrically unibranch and henselian, which affords a characterization of representable sheaves.