Note on algebraic irregular Riemann-Hilbert correspondence

The subject of this paper is an algebraic version of the irregular Riemann-Hilbert correspondence which was mentioned in [Tsukuba J. Math. 44 (2020), 155-201]. In particular, we prove an equivalence of categories between the triangulated category Dbhol(DX) of holonomic D-modules on a smooth algebraic variety X over C and the triangulated category EbC-c(ICX1) of algebraic C-constructible enhanced ind-sheaves on a bordered space Xan1. Moreover, we show that there exists a t-structure on the triangulated category EbC-c (ICX1) whose heart is equivalent to the abelian category of holonomic D-modules on X. Furthermore, we shall consider simple objects of its heart and minimal extensions of objects of its heart.