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Kloosterman sums and monodromy of a \(p\)-adic hypergeometric equation. (English) Zbl 0806.14018
The paper under review computes the overconvergent and convergent differential Galois-groups associated to Kloosterman sums, in characteristic \(p>2\). In the overconvergent case one obtains the same groups as in the étale \(l\)-adic cohomology (as computed by N. Katz), in the convergent Borel-subgroups of these. The main technical tool is the comparison of Frobenius-elements and thus a reduction to the \(l\)-adic case. On the way the author verifies various conjectures about overconvergence in this operial case.
Reviewer: G.Faltings (Bonn)

MSC:
14F30 \(p\)-adic cohomology, crystalline cohomology
14G20 Local ground fields in algebraic geometry
33C80 Connections of hypergeometric functions with groups and algebras, and related topics
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References:
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