The flatness of the $\mathcal O$-module of smooth functions and integral representation

Artikel i vetenskaplig tidskrift, 2022

We give a proof of the well-known fact that the $\Ok$-module $\E$ of smooth functions is flat

by means of residue theory and integral formulas.  A variant of the proof gives  

a related statement for

classes of functions of lower regularity. We also prove a Brian\c con-Skoda type theorem for

ideals of the form $\E a$, where $a$ is an ideal in $\Ok$.