$\mathbb{C}$-Constructible enhanced ind-sheaves

Abstract

A. D'Agnolo and M. Kashiwara proved that their enhanced solution functor induces a fully faithful embedding of the triangulated category of holonomic $\cal D$-modules into the one of $\mathbb{R}$-constructible enhanced ind-sheaves. In this paper, we introduce a notion of $\mathbb{C}$-constructible enhanced ind-sheaves and show that the triangulated category of them is equivalent to its essential image. Moreover we show that there exists a t-structure on it whose heart is equivalent to the abelian category of holonomic $\cal D$-modules.