Document Type


Publication Date



In this paper we prove that the projective dimension of Mn = R^4/(An) is 2n -1, where R is the ring of polynomials in 4n variables with complex coefficients and (An) is the module generated by the columns of a 4x4n matrix which arises as the Fourier transform of the matrix of differential operators associated with the regularity condition for a function of n quaternionic variables. As a corollary we show that the sheaf R of regular functions has flabby dimension 2n -1, and we prove a cohomology vanishing theorem for open sets in the space Hn of quaternions. We also show that Ext3(Mn, R) = 0, for j = 1,...., 2n - 2, and Ext ^(2n -1) (Mn, R) =/= 0, and we use this result to show the removability of certain singularities of the Cauchy Fueter system.


This article was originally published in Annales de l'Institut Fourier, volume 47, issue 2, in 1997.

Peer Reviewed



L'Institut Fourier



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.