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Transactions of the American Mathematical Society

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Simple holonomic modules over rings of differential operators with regular coefficients of Krull dimension 2

Authors: V. Bavula and F. van Oystaeyen
Journal: Trans. Amer. Math. Soc. 353 (2001), 2193-2214
MSC (2000): Primary 16S32, 32C38, 13N10
Published electronically: January 29, 2001
MathSciNet review: 1814067
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Let $K$ be an algebraically closed field of characteristic zero. Let $\Lambda $ be the ring of ($K$-linear) differential operators with coefficients from a regular commutative affine domain of Krull dimension $2$ which is the tensor product of two regular commutative affine domains of Krull dimension $1$. Simple holonomic $\Lambda$-modules are described. Let a $K$-algebra $D$ be a regular affine commutative domain of Krull dimension $1$ and ${\cal D} (D)$ be the ring of differential operators with coefficients from $D$. We classify (up to irreducible elements of a certain Euclidean domain) simple ${\cal D}(D)$-modules (the field $K$ is not necessarily algebraically closed).

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Additional Information

V. Bavula
Affiliation: Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH, UK

F. van Oystaeyen
Affiliation: Department of Mathematics and Computer Science, University of Antwerp (U.I.A), Universiteitsplein, 1, B-2610, Wilrijk, Belgium

Received by editor(s): September 15, 1998
Received by editor(s) in revised form: March 23, 2000
Published electronically: January 29, 2001
Additional Notes: The first author was supported by a grant of the University of Antwerp as a research fellow at U.I.A
Article copyright: © Copyright 2001 American Mathematical Society