In [Ito24a], the author explained a relation between enhanced ind-sheaves and enhanced subanalytic sheaves. In particular, a relation between [DK16, Thm. 9.5.3] and [Kas16, Thm. 6.3] had been explained. Moreover, in [Ito24b], 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.

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Enhanced Perverse Subanalytic Sheaves

  • Ito Yohei

摘要

In [Ito24a], the author explained a relation between enhanced ind-sheaves and enhanced subanalytic sheaves. In particular, a relation between [DK16, Thm. 9.5.3] and [Kas16, Thm. 6.3] had been explained. Moreover, in [Ito24b], 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.