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Étale covers, bimodules and differential operators. (English) Zbl 0807.13011

Let \(R\) be a Dedekind domain, finitely generated over \(k\), an algebraically closed field of characteristic zero. Let \({\mathcal D} (R)\) be the ring of differential operators on \(R\). Let \(S\) be a domain and \(G\) a finite, soluble subgroup of \(\operatorname{Aut}_ k S\) such that \(S^ G \cong {\mathcal D} (R)\). We show that there exists an étale extension \(R_ 1\) of \(R\), with Galois group \(G\), such that \(S \cong {\mathcal D} (R_ 1)\).

MSC:

13N10 Commutative rings of differential operators and their modules
13F05 Dedekind, Prüfer, Krull and Mori rings and their generalizations
13B05 Galois theory and commutative ring extensions
14L24 Geometric invariant theory
13A50 Actions of groups on commutative rings; invariant theory
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References:

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