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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

Citations:

Zbl 0796.12005
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References:

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