Let Σ be a finite regular cell complex with ∅ ∈ Σ, and regard it as a poset (i.e., partially ordered set) by inclusion. Let R be the incidence algebra of the poset Σ over a field k. Corresponding to the Verdier duality for constructible sheaves on Σ, we have a dualizing complex ω ∈ Db(modR⊗kR) giving a duality functor from Db(modR) to itself. This duality is somewhat analogous to the Serre dual...

We formulate and study a new coarse (co-)assembly map. It involves a modification of the Higson corona construction and produces a map dual in an appropriate sense to the standard coarse assembly map. The new assembly map is shown to be an isomorphism in many cases. For the underlying metric space of a group, the coarse co-assembly map is closely related to the existence of a dual Dirac morphis...

Let $(R, m)$ be a commutative noetherian local ring and let $Gamma$ be a finite group. It is proved that if $R$ admits a dualizing module, then the group ring $Rga$ has a dualizing bimodule as well. Moreover, it is shown that a finitely generated $Rga$-module $M$ has generalized Gorenstein dimension zero if and only if it has generalized Gorenstein dimension zero as an $R$-module.

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...

We develop a theory of residues for arithmetic surfaces, establish the reciprocity law around a point, and use the residue maps to explicitly construct the dualizing sheaf of the surface. These are generalisations of known results for surfaces over a perfect field. In an appendix, explicit local ramification theory is used to recover the fact that in the case of a local complete intersection th...

It has been known since the work of Carlsson [2] and Weinshall [17] that there is a dualization principle that allows one to interchange the role of points being viewed by several cameras and the camera centres themselves. In principle this implies the possibility of dualizing projective reconstruction algorithms to obtain new algorithms. In this paper, this theme is developed at a theoretical ...

To an inclusion H ⊂ G of topological groups, we associate a spectrum DH⊂G, which coincides with the dualizing spectrum DG of [K4] when H = G. We also introduce a fibered spectrum analogue. The main application is to give a purely homotopy theoretic construction of Poincaré embeddings in stable codimension.