Cohomological interpretation of hypergeometric series (Q1315177)

This paper explains, once again, how to get a cohomological interpretation of generalized hypergeometric series in several variables by means of ``exponential modules'' [for instance, see the author and \textit{F. Loeser}, Jap. J. Math., New Ser. 19, 81-129 (1993; Zbl 0796.12005)] under some restrictive hypotheses. Even if yet rather computational, the new proof given here is more elementary than the older ones. It is based on a beautiful proposition which looks like a generalized division process. (Counter)-examples are given which throw light on the situation and on the particular case where restrictive hypotheses are not satisfied.