Enhanced Perverse Subanalytic Sheaves
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913753552912384 |
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| author | Ito, Yohei |
| author_facet | Ito, Yohei |
| contents | In [arXiv:2109.13991], the author explained a relation between enhanced ind-sheaves and enhanced subanalytic sheaves. In particular, a relation between [Thm.9.5.3, Andrea D'Agnolo and Masaki Kashiwara, Riemann-Hilbert correspondence for holonomic $\mathcal{D}$-modules, 2016] and [Thm.6.3, Masaki Kashiwara, Riemann-Hilbert correspondence for irregular holonomic $\mathcal{D}$-modules, 2016] had been explained. Moreover, in [arXiv:2310.19501], the author defined $\mathbb{C}$-constructibility for enhanced subanalytic sheaves and proved that there exists an equivalence of categories between the triangulated category of holonomic $\mathcal{D}$-modules and that of $\mathbb{C}$-constructible enhanced subanalytic sheaves. In this paper, we will show that there exists a t-structure on the triangulated category of $\mathbb{C}$-constructible enhanced subanalytic sheaves whose heart is equivalent to the abelian category of holonomic $\mathcal{D}$-modules. Furthermore, we shall consider simple objects of its heart and minimal extensions of objects of its heart. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_17747 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Enhanced Perverse Subanalytic Sheaves Ito, Yohei Algebraic Geometry 18F10, 32C38, 35Q15, 32S60 In [arXiv:2109.13991], the author explained a relation between enhanced ind-sheaves and enhanced subanalytic sheaves. In particular, a relation between [Thm.9.5.3, Andrea D'Agnolo and Masaki Kashiwara, Riemann-Hilbert correspondence for holonomic $\mathcal{D}$-modules, 2016] and [Thm.6.3, Masaki Kashiwara, Riemann-Hilbert correspondence for irregular holonomic $\mathcal{D}$-modules, 2016] had been explained. Moreover, in [arXiv:2310.19501], the author defined $\mathbb{C}$-constructibility for enhanced subanalytic sheaves and proved that there exists an equivalence of categories between the triangulated category of holonomic $\mathcal{D}$-modules and that of $\mathbb{C}$-constructible enhanced subanalytic sheaves. In this paper, we will show that there exists a t-structure on the triangulated category of $\mathbb{C}$-constructible enhanced subanalytic sheaves whose heart is equivalent to the abelian category of holonomic $\mathcal{D}$-modules. Furthermore, we shall consider simple objects of its heart and minimal extensions of objects of its heart. |
| title | Enhanced Perverse Subanalytic Sheaves |
| topic | Algebraic Geometry 18F10, 32C38, 35Q15, 32S60 |
| url | https://arxiv.org/abs/2503.17747 |