Geodesic
Note on algebraic irregular Riemann–Hilbert correspondence
Rendiconti del Seminario Matematico della Università di Padova, Tome 149 (2023), pp. 45-81

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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.

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DOI : 10.4171/rsmup/119
Classification : 18 
Ito, Yohei. Note on algebraic irregular Riemann–Hilbert correspondence. Rendiconti del Seminario Matematico della Università di Padova, Tome 149 (2023), pp. 45-81. doi: 10.4171/rsmup/119
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     title = {Note on algebraic irregular {Riemann{\textendash}Hilbert} correspondence},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {45--81},
     year = {2023},
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     doi = {10.4171/rsmup/119},
     mrnumber = {4575364},
     zbl = {07688317},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/rsmup/119/}
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