Publications of the Research Institute for Mathematical Sciences


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Volume 47, Issue 1, 2011, pp. 221–255
DOI: 10.2977/PRIMS/35

Published online: 2011-03-24

Regular holonomic $\mathscr{D}{[\mspace{-1mu}[\hbar]\mspace{-1mu}]}$-modules

Andrea D'Agnolo[1], Stéphane Guillermou[2] and Pierre Schapira[3]

(1) Università di Padova, Italy
(2) Université de Grenoble I, Saint-Martin-d'Hères, France
(3) Université Pierre et Marie Curie, Paris, France

We describe the category of regular holonomic modules over the ring $\mathscr{D}{[\mspace{-1mu}[\hbar]\mspace{-1mu}]}$ of linear differential operators with a formal parameter $\hbar$. In particular, we establish the Riemann-Hilbert correspondence and discuss the additional $t$-structure related to $\hbar$-torsion.

Keywords: D-modules, deformation-quantization, Riemann–Hilbert correspondence, torsion pairs

D'Agnolo Andrea, Guillermou Stéphane, Schapira Pierre: Regular holonomic $\mathscr{D}{[\mspace{-1mu}[\hbar]\mspace{-1mu}]}$-modules. Publ. Res. Inst. Math. Sci. 47 (2011), 221-255. doi: 10.2977/PRIMS/35