## Arkiv för Matematik

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

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

Rolf Källström

#### Abstract

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

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

Dates
Revised: 18 May 2013
First available in Project Euclid: 30 January 2017

https://projecteuclid.org/euclid.afm/1485802678

Digital Object Identifier
doi:10.1007/s11512-013-0186-z

Mathematical Reviews number (MathSciNet)
MR3255141

Zentralblatt MATH identifier
1312.13030

Rights
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. https://projecteuclid.org/euclid.afm/1485802678