Another proof of the Riemann-Hilbert Correspondence for Regular Holonomic D-Modules

Abstract: In this paper, we reprove the Riemann-Hilbert correspondence for regular holonomic D-modules of M. Kashiwara, Publ. Res. Inst. Math. Sci., 1984 by using the irregular Riemann-Hilbert correspondence of [A. D'Agnolo and M. Kashiwara, Publ. Math. Inst. Hautes Etudes Sci., 2016]. Moreover, we also prove the algebraic one by the same argument. For this purpose, we study C-constructible enhanced ind-sheaves of [Y. Ito, Tsukuba journal of Mathematics, 2020, Rend. Sem. Mat. Univ. Padova., 2021.] in more detail.