Enhanced perversities

TL;DR

This paper introduces a middle perversity t-structure on the category of enhanced ind-sheaves and proves the Riemann-Hilbert correspondence embedding is exact with respect to this new structure.

Contribution

It establishes a new middle perversity t-structure on enhanced ind-sheaves and demonstrates the exactness of the Riemann-Hilbert correspondence embedding.

Findings

The embedding of holonomic D-modules into enhanced ind-sheaves is exact under the new t-structure.

A middle perversity t-structure is constructed on the target category.

The work extends the Riemann-Hilbert correspondence to a new t-structure setting.

Abstract

The Riemann-Hilbert correspondence embeds the triangulated category of (not necessarily regular) holonomic D-modules into that of $\mathbb R$-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.