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Yohei Ito

Publications and source records attributed to Yohei Ito.

9 recordsLinked to original sources
arXiv2025

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.

math.AG↗
arXiv2023

Finiteness properties of Ind-Sheaves with Ring Actions

In this paper, we shall consider some finiteness of ind-sheaves with ring actions. As the main result of this paper, there exists an equivalence of categories between the abelian category of coherent ind-$\beta\mathcal{A}$-modules and the one of coherent $\mathcal{A}$-modules, where $\mathcal{A}$ is a sheaf of k-algebras and $\Bbbk$ is a field.

math.AG↗
arXiv2023

Irregular Riemann-Hilbert Correspondence and Enhanced Subanalytic Sheaves

In [arXiv:2109.13991], the author explained a relation between enhanced ind-sheaves and enhanced subanalytic sheaves. In this paper, we shall define C-constructability for enhanced subanalytic sheaves which was announced in [arXiv:2109.13991], and show that there exists an equivalence of categories between the triangulated category of C-constructible enhanced subanalytic sheaves and the one of holonomic D-modules.

math.AG↗
arXiv2023

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

In this paper, we reprove the Riemann-Hilbert correspondence for regular holonomic D-modules of [M. Kashiwara, Publ. Res. Inst. Math. Sci., 1984] (see also [Z. Mebkhout, Compositio Math., 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.

math.AG↗
arXiv2021

Note on Relation between Enhanced Ind-Sheaves and Enhanced Subanalytic Sheaves

In this paper, we will explain a relation between [Thm. 9.5.3, Andrea D'Agnolo and Masaki Kashiwara, Riemann-Hilbert correspondence for holonomic D-modules, 2016] and [Thm. 6.3, Masaki Kashiwara, Riemann-Hilbert correspondence for irregular holonomic D-modules]. For this purpose, we will also explain a relation between enhanced ind-sheaves and enhanced subanalytic sheaves.

math.AG↗
arXiv2020

Note On The Algebraic Irregular Riemann-Hilbert Correspondence

The subject of this paper is an algebraic version of the irregular Riemann-Hilbert correspondence which was mentioned in [arXiv:1910.09954] by the author. In particular, we prove an equivalence of categories between the triangulated category of algebraic holonomic D-modules on a smooth algebraic variety and the one of algebraic C-constructible enhanced ind-sheaves. Moreover we show that there exists a t-structure on the triangulated category of algebraic C-constructible enhanced ind-sheaves whose heart is equivalent to the abelian category of algebraic holonomic D-modules. Furthermore we shall consider simple objects of its heart and minimal extensions of objects of its heart.

math.AG↗
arXiv2020

C-Constructible Enhanced Ind-Sheaves

A. D'Agnolo and M. Kashiwara proved that their enhanced solution functor induces a fully faithful embedding of the triangulated category of holonomic D-modules into the one of R-constructible enhanced ind-sheaves. In this paper, we define C-constructible enhanced ind-sheaves and show that the triangulated category of them is equivalent to its essential image. Moreover we show that there exists a t-structure on it whose heart is equivalent to the abelian category of holonomic D-modules.

math.AG↗
arXiv2020

On Irregularities of Fourier Transforms of Regular Holonomic D-Modules

We study Fourier transforms of regular holonomic D-modules. By using the theory of Fourier-Sato transforms of enhanced ind-sheaves developed by Kashiwara-Schapira and D'Agnolo-Kashiwara, a formula for their enhanced solution complexes will be obtained. Moreover we show that some parts of their characteristic cycles and irregularities are expressed by the geometries of the original D-modules.

math.AG↗