In this paper we prove the preconstructibility of the complex of tempered holomorphic solutions of holonomic D-modules on complex analytic manifolds. This implies the finiteness of such complex on any relatively compact open subanalytic subset of a complex analytic manifold. Such a result is an essential step for proving a conjecture of M. Kashiwara and P. Schapira (2003) on the constructibility of such complex.
Constructibility of tempered solutions of holonomic D-modules
Tempered solutions of $\mathcal D$-modules on complex curves and formal invariants
Formal structure of direct image of holonomic D-modules of exponential type
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