A Direct Proof of the Theorem on Formal Functions

TL;DR

This paper provides a straightforward and elementary proof of the theorem on formal functions by examining how the Godement resolution of a sheaf of modules behaves under completion.

Contribution

It offers a direct proof of the theorem on formal functions, simplifying previous approaches through an analysis of sheaf resolutions and completion.

Findings

Proof simplifies understanding of the theorem on formal functions

Demonstrates the behavior of sheaf resolutions under completion

Provides an elementary approach to a classical theorem

Abstract

We give a direct and elementary proof of the theorem on formal functions by studying the behaviour of the Godement resolution of a sheaf of modules under completion.