Related papers: Duality in tensor-triangular geometry via proxy-sm…
We introduce a new, algebraic method to construct duality functions for integrable dynamic models. This method will be implemented on dynamic stochastic higher spin vertex models, where we prove the duality functions are the $ _3 \varphi_2$…
Davydov--Yetter (DY) cohomology classifies infinitesimal deformations of the monoidal structure of tensor functors and tensor categories. In this paper we provide new tools for the computation of the DY cohomology for finite tensor…
We present some results on equivariant KK-theory in the context of tensor triangular geometry. More specifically, for G a finite group, we show that the spectrum of the tensor triangulated subcategory of KK^G generated by the tensor unit…
This thesis is comprised of three chapters. The first chapter deals with bounded complexes of Gorenstein projective and Gorenstein injective modules. Deploying methods of relative homological algebra, we approximate such complexes with…
In this paper we obtain a description of the Grothendieck group of complex vector bundles over the classifying space of a p-local finite group in terms of representation rings of subgroups of its Sylow. We also prove a stable elements…
The aim of this paper is to study the $w^*$-fixed point property for nonexpansive mappings in the duals of separable Lindenstrauss spaces by means of suitable geometrical properties of the dual ball. First we show that a property concerning…
Exploiting the special features of four-dimensional Riemannian geometry, we derive topological and rigidity results for hypersurfaces immersed in space forms of dimension 5. First, we provide a complete description of the Weyl tensor for…
In this paper, we systematically apply Grothendieck duality theorem to simplify the proofs of several theorems in different papers: Including a vanishing theorem in KMM, a theorem of Koll\'{a}r's paper, a vanishing theorem due to Kov\'{a}cs…
We develop the Dirac-Schwinger-Zwanziger (DSZ) quantization of classical abelian gauge theories with general duality structure on oriented Lorentzian four-manifolds $(M,g)$ of arbitrary topology, obtaining, as a result, the…
We establish a partial extension of the Poincar\'e duality theorem of Jell-Rau-Shaw to tropical hypersurfaces arising from non-primitive triangulations. We introduce a notion of level of primitivity for triangulations of lattice polytopes…
This paper generalizes the normally ordered tensor product from Tate vector spaces to Tate objects over arbitrary exact categories. We show how to lift bi-right exact monoidal structures, duality functors, and construct external Homs. We…
This paper will generalize what may be termed the "geometric duality theory" of real pre-ordered Banach spaces which relates geometric properties of a closed cone in a real Banach space, to geometric properties of the dual cone in the dual…
Classical linearized gravity admits a dual formulation in terms of a higher-rank tensor field. Proposing a prescription for the instanton sectors of linearized gravity and its dual, we show that they may be quantum inequivalent in even…
Tensor triangular geometry as introduced by Balmer is a powerful idea which can be used to extract the ambient geometry from a given tensor triangulated category. In this paper we provide a general setting for a compactly generated tensor…
In this paper we treat Grothendieck Duality for noetherian rings via rigid dualizing complexes. In particular, we prove that every ring, essentially finite type over a regular base ring, has a unique rigid dualizing complex. The rigid…
Codensity monads provide a universal method to generate complex monads from simple functors. Recently, a wide range of important monads in logic, denotational semantics, and probabilistic computation, such as several incarnations of the…
The aim of these notes, originally intended as an appendix to a book on the foundations of equivariant cohomology, is to set up the formalism of the $G$-equivariant Poincar\'e duality for oriented $G$-manifolds, for any connected compact…
This paper addresses the study and applications of polyhedral duality of locally convex topological vector (LCTV) spaces. We first revisit the classical Rockafellar's proper separation theorem for two convex sets one which is polyhedral and…
We extend the duality between massive and topologically massive antisymmetric tensor gauge theories in arbitrary space-time dimensions to include topological defects. We show explicitly that the condensation of these defects leads, in 4…
An equivariant version of the twisted inverse pseudofunctor is defined, and equivariant versions of some important properties, including the Grothendieck duality of proper morphisms and flat base change are proved. As an application, a…