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

Bavula, V.; van Oystaeyen, F.

doi:10.1090/S0002-9947-01-02701-5

Simple holonomic modules over rings of differential operators with regular coefficients of Krull dimension 2
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Trans. Amer. Math. Soc. 353 (2001), 2193-2214 Request permission

Abstract:

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 $\mathcal {D} (D)$ be the ring of differential operators with coefficients from $D$. We classify (up to irreducible elements of a certain Euclidean domain) simple $\mathcal {D}(D)$-modules (the field $K$ is not necessarily algebraically closed).

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