Rigid Dualizing Complexes on Schemes
نویسنده
چکیده
In this paper we present a new approach to Grothendieck duality on schemes. Our approach is based on the idea of rigid dualizing complexes, which was introduced by Van den Bergh in the context of noncommutative algebraic geometry. We obtain most of the important features of Grothendieck duality, yet manage to avoid lengthy and difficult compatibility verifications. Our results apply to finite type schemes over a regular noetherian finite dimensional base ring, and hence are suitable for arithmetic geometry.
منابع مشابه
RIGID DUALIZING COMPLEXES
Let $X$ be a sufficiently nice scheme. We survey some recent progress on dualizing complexes. It turns out that a complex in $kinj X$ is dualizing if and only if tensor product with it induces an equivalence of categories from Murfet's new category $kmpr X$ to the category $kinj X$. In these terms, it becomes interesting to wonder how to glue such equivalences.
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In this paper we present a new approach to Grothendieck duality over commutative rings. Our approach is based on the idea of rigid dualizing complexes, which was introduced by Van den Bergh in the context of noncommutative algebraic geometry. We obtain many of the important local features of Grothendieck duality, yet manage to avoid lengthy and difficult compatibility verifications. Our results...
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Let A be a commutative ring, B a commutative A-algebra and M a complex of B-modules. We begin by constructing the square SqB/A M , which is also a complex of B-modules. The squaring operation is a quadratic functor, and its construction requires differential graded (DG) algebras. If there exists an isomorphism ρ : M ≃ −→ SqB/A M then the pair (M,ρ) is called a rigid complex over B relative to A...
متن کاملar X iv : m at h / 06 01 65 4 v 2 [ m at h . A G ] 2 8 Ju l 2 00 6 RIGID DUALIZING COMPLEXES OVER COMMUTATIVE RINGS
In this paper we present a new approach to Grothendieck duality over commutative rings. Our approach is based on the idea of rigid dualizing complexes, which was introduced by Van den Bergh in the context of noncommutative algebraic geometry. The method of rigidity was modified to work over general commutative base rings in our paper [YZ5]. In the present paper we obtain many of the important l...
متن کاملar X iv : m at h / 06 03 73 3 v 2 [ m at h . A C ] 1 9 Ju n 20 06 RIGID COMPLEXES VIA DG ALGEBRAS
Let A be a commutative ring, B a commutative A-algebra and M a complex of B-modules. We begin by constructing the square SqB/A M , which is also a complex of B-modules. The squaring operation is a quadratic functor, and its construction requires differential graded (DG) algebras. If there exists an isomorphism ρ : M ≃ −→ SqB/A M then the pair (M,ρ) is called a rigid complex over B relative to A...
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