Enhanced Perverse Subanalytic Sheaves

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.

Publication Details

Journal
ArXiv.org
Published
2025-03-22
Primary Topic
Algebraic structures and combinatorial models
Type
article
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article

Enhanced Perverse Subanalytic Sheaves

ArXiv.org
Algebraic structures and combinatorial models
article

Enhanced Perverse Subanalytic Sheaves

article en

Abstract

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.

ArXiv.org
Openalex Percentile: Top 42%
Algebraic structures and combinatorial models
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