相关论文: A Generalization of the Greene-Kleitman Duality Th…

This expository article delves into the Greenlees-May Duality Theorem which is widely thought of as a far-reaching generalization of the Grothendieck's Local Duality Theorem. This theorem is not addressed in the literature as it merits and…

We develop Morse-Bott theory on posets, generalizing both discrete Morse-Bott theory for regular complexes and Morse theory on posets. Moreover, we prove a Lusternik-Schnirelmann theorem for general matchings on posets, in particular, for…

We develop Grothendieck's theory of dualizing complexes on finite posets, and its subsequent theory of Cohen-Macaulayness.

We prove a duality theorem for Cohen--Macaulay simplicial complexes. This is a generalisation of Poincar\'e Duality, framed in the language of combinatorial sheaves. Our treatment is self-contained and accessible for readers with a working…

We prove a duality theorem for graded algebras over a field that implies several known duality results : graded local duality, versions of Serre duality for local cohomology and of Suzuki duality for generalized local cohomology, and…

Using Dold--Puppe category approach to the duality in topology, we prove general duality theorem for the category of motives. As one of the applications of this general result we obtain, in particular, a generalization of…

The purpose of this paper is to generalize the self-duality equation by Tchrakian and Corrigan et. al.. Novel generalized self-duality equations on higher-dimensional spaces are discussed. This class of equations includes the usual…

We generalize the Giveon-Kutasov duality by adding possible Chern-Simons interactions for the $U(N)$ gauge group. Some of the generalized dualities are known in the literature and many others are new to the best of our knowledge. The…

We give a new proof of a recent result due to Mats Andersson and Elizabeth Wulcan, generalizing the local Grothendieck duality theorem. It can also be seen as a generalization of a previous result by Mikael Passare. Our method does not…

The work is my Ph D thesis (dissertation for obtaining candidate of sciences degree in Russia) fulfilled under direction of D. A. Raikov and defended under supervision of N. Ya. Vilenkin and S. V. Ptchelintsev. In the dissertatin I gave…

We generalize the Galileon duality to any single scalar field Lagrangian coupled locally to any matter field. Under the duality, a generalized Galileon maps into another generalized Galileon via a one parameter group of transformations,…

We prove a number of dualities between posets and (pseudo)bases of open sets in locally compact Hausdorff spaces. In particular, we show that (1) Relatively compact basic sublattices are finitely axiomatizable. (2) Relatively compact basic…

We establish duality results for the cohomology of the Weil group of a $p$-adic field, analogous to, but more general than, results from Galois cohomology. We prove a duality theorem for discrete Weil modules, which implies Tate-Nakayama…

We formulate and study an extension of gerbe duality to relative Gromov-Witten theory.

In this paper, we generalize the duality between self-dual and Maxwell-Chern-Simons theories for the case of a CPT-even Lorentz-breaking extension of these theories. The duality is demonstrated with use of the gauge embedding procedure,…

We prove a new duality theorem for the category of precontact algebras which implies the Stone Duality Theorem, its connected version obtained in arXiv:1508.02220v3, 1-44 (to appear in Topology Appl.), the recent duality theorems of…

We give an alternative, more geometric, proof of the well-known Joyal-Tierney Theorem in locale theory by utilizing Priestley duality for frames.

We discuss two known sheaf-cosheaf duality theorems: Curry's for the face posets of finite regular CW complexes and Lurie's for compact Hausdorff spaces, i.e., covariant Verdier duality. We provide a uniform formulation for them and prove…

We consider versions of the local duality theorem in $\mathbb{C}^n$. We show that there exist canonical pairings in these versions of the duality theorem which can be expressed explicitly in terms of residues of Grothendieck, or in terms of…

A general non-relativistic field theory on the plane with couplings to an arbitrary number of abelian Chern-Simons gauge fields is considered. Elementary excitations of the system are shown to exhibit fractional and mutual statistics. We…