A Gevrey Differential Complex on the Torus.

To a system of n closed one-forms on the torus T m + n , we associate a differential complex and compute the induced cohomology groups in the s-Gevrey category, provided that a related matrix of periods satisfies a Diophantine condition. Also, we present a complete characterization for the s-global hypoellipticity at the level of q-forms for q ≥ 0 . [ABSTRACT FROM AUTHOR]