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Self-dual t-structure. (English) Zbl 1355.18008

This paper constructs a self-dual t-structure on the derived category of \(\mathbb{R}\)-constructible sheaves on a real analytic manifold. Here self-duality means the one with respect to the Verdier dual functor, and a t-structure is not the ordinary one but a generalized one.
The main construction is presented in section 5 after the introduction of the generalized t-structure in section 1. This generalized t-structure is actually a part of the Bridgeland stability condition.
This paper also studies other examples of self-dual generalized t-structures, such as one on the derived category of coherent sheaves on a Noetherian regular scheme in Section 4, and one on the derived category of the abelian category of sheaves of modules over Noetherian regular ring on a complex manifold with \(\mathbb{C}\)-constructible cohomology in Section 6.
The presentation and texts are clearly and carefully written. Almost all the prerequisite knowledge appear in [M. Kashiwara and P. Schapira, Sheaves on manifolds. With a short history “Les débuts de la théorie des faisceaux” by Christian Houzel. Berlin etc.: Springer-Verlag (1990; Zbl 0709.18001)].

MSC:

18E30 Derived categories, triangulated categories (MSC2010)

Keywords:

t-structure

Citations:

Zbl 0709.18001
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