Arkiv för Matematik

  • Ark. Mat.
  • Volume 52, Number 2 (2014), 291-299.

$\mathcal{D}$-modules with finite support are semi-simple

Rolf Källström

Full-text: Open access


Let $(R, \frak{m}, k_{R})$ be a regular local k-algebra satisfying the weak Jacobian criterion, and such that kR/k is an algebraic field extension. Let $\mathcal{D}_{R}$ be the ring of k-linear differential operators of R. We give an explicit decomposition of the $\mathcal{D}_{R}$-module $\mathcal{D}_{R}/\mathcal{D}_{R} \frak{m}_{R}^{n+1}$ as a direct sum of simple modules, all isomorphic to $\mathcal{D}_{R}/\mathcal{D}_{R} \frak{m}$, where certain “Pochhammer” differential operators are used to describe generators of the simple components.

Article information

Ark. Mat., Volume 52, Number 2 (2014), 291-299.

Received: 20 August 2012
Revised: 18 May 2013
First available in Project Euclid: 30 January 2017

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

2013 © Institut Mittag-Leffler


Källström, Rolf. $\mathcal{D}$-modules with finite support are semi-simple. Ark. Mat. 52 (2014), no. 2, 291--299. doi:10.1007/s11512-013-0186-z.

Export citation


  • Borel, A., Grivel, P.-P., Kaup, B., Haefliger, A., Malgrange, B. and Ehlers, F., AlgebraicD-Modules, Perspectives in Mathematics 2, Academic Press, Boston, MA, 1987
  • Grothendieck, A., Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes de schémas, Publ. Math. Inst. Hautes Études Sci. 32 (1967), 1–361.
  • Källström, R. and Tadesse, Y., Hilbert series of modules over Lie algebroids, Preprint, 2011.
  • Matsumura, H., Commutative Ring Theory, Cambridge University Press, Cambridge, 1986
  • Stafford, J. T., Module structure of Weyl algebras, J. Lond. Math. Soc. 18 (1978), 429–442.