On a complex manifold, the Riemann–Hilbert correspondence embeds the triangulated category of (not necessarily regular) holonomic -modules into the triangulated category of -constructible enhanced ind-sheaves. The source category has a standard t-structure. Here, we provide the target category with a middle perversity t-structure, and prove that the embedding is exact.
In the paper, we also discuss general perversities in the framework of -constructible enhanced ind-sheaves on bordered subanalytic spaces.
Funding source: Japan Society for the Promotion of Science
Award Identifier / Grant number: 15H03608
Funding source: Università degli Studi di Padova
Award Identifier / Grant number: CPDA159224
Funding statement: The first author was partially supported by grant CPDA159224, Padova University. The second author was supported by Grant-in-Aid for Scientific Research (B) 15H03608, Japan Society for the Promotion of Science.
The first author acknowledges the kind hospitality at RIMS, Kyoto University, during the preparation of this paper.
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