Note on algebraic irregular Riemann–Hilbert correspondence

Ito, Yohei

Rendiconti del Seminario Matematico della Università di Padova, Tome 149 (2023), pp. 45-81.

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 𝐃 hol b (𝒟 X ) of holonomic 𝒟-modules on a smooth algebraic variety X over ℂ and the triangulated category $\mathbf{E}^{\mathrm{b}}_{\operatorname{\mathbb{C}-c}}( \mathrm{I}\mathbb{C}_{X_\infty})$ of algebraic ℂ-constructible enhanced ind-sheaves on a bordered space X ∞ an. Moreover, we show that there exists a t-structure on the triangulated category $\mathbf{E}^{\mathrm{b}}_{\operatorname{\mathbb{C}-c}}(\mathrm{I}\mathbb{C}_{X_\infty})$ 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.

Classification : 18