The flatness of the $\mathcal O$-module of smooth functions and integral representation
Journal article, 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 $\Ok$.
ideals of the form $\E a$, where $a$ is an ideal in $\Ok$.
Integral formula, flatness
Author
Mats Andersson
University of Gothenburg
Chalmers, Mathematical Sciences, Algebra and geometry
Annales de la Faculté des Sciences de Toulouse
2258-7519 (ISSN)
Vol. XXXII 1 1-14Subject Categories (SSIF 2011)
Algebra and Logic
Geometry
Mathematical Analysis
DOI
10.5802/afst.1725