## Cohomological interpretation of hypergeometric series.(English)Zbl 0808.12006

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 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.
Reviewer: G.Christol (Paris)

### MSC:

 12H25 $$p$$-adic differential equations 33C70 Other hypergeometric functions and integrals in several variables 14F30 $$p$$-adic cohomology, crystalline cohomology

Zbl 0796.12005
Full Text:

### References:

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