Related papers: Stone duality for spectral sheaves and the patch m…
We introduce a notion of Homological Projective Duality for smooth algebraic varieties in dual projective spaces, a homological extension of the classical projective duality. If algebraic varieties $X$ and $Y$ in dual projective spaces are…
We study some natural generalizations of the spectral spaces in the contexts of commutative rings and distributive lattices. We obtain a topological characterization for the spectra of commutative (not necessarily unitary) rings and we find…
Scaffolds are certain tensors arising in the study of association schemes, and have been (implicitly) understood diagrammatically as digraphs with distinguished "root" nodes and with matrix edge weights, often taken from Bose-Mesner…
We establish a duality between monads and monadic morphisms in any $(\infty,2)$-category and characterize monadic morphisms in a wide class of examples. This duality unifies several dualities between algebraic structures and their…
We study the dualizability of sheaves on manifolds with isotropic singular supports $\operatorname{Sh}_\Lambda(M)$ and microsheaves with isotropic supports $\operatorname{\mu sh}_\Lambda(\Lambda)$ and obtain a classification result of…
Our aim is to give some insights about how to approach the formal description of situations where one has to conciliate several contradictory statements, rules, laws or ideas. We show that such a conciliation structure can be naturally…
We display a symmetric monoidal equivalence between the stable $\infty$-category of filtered spectra, and quasi-coherent sheaves on $\mathbb{A}^1 / \mathbb{G}_m$, the quotient in the setting of spectral algebraic geometry, of the flat…
We prove versions of the spectral adjunction, a Stone-type duality and Hofmann-Lawson duality for locally small spaces with bounded continuous mappings.
We study the notion of duality in the context of graded manifolds. For graded bundles, somehow like in the case of Gelfand representation and the duality: points vs. functions, we obtain natural dual objects which belongs to a different…
We formulate and prove the existence of an asymptotic duality along the fibers of the Green-Griffiths jet bundles over projective manifolds. The existence of global sections for these bundles and also for their dual sheaves has been…
A common feature of many duality results is that the involved equivalence functors are liftings of hom-functors into the two-element space resp. lattice. Due to this fact, we can only expect dualities for categories cogenerated by the…
In the prequel to this paper, two versions of Le Potier's strange duality conjecture for sheaves over abelian surfaces were studied. A third version is considered here. In the current setup, the isomorphism involves moduli spaces of sheaves…
We study representations of MV-algebras -- equivalently, unital lattice-ordered abelian groups -- through the lens of Stone-Priestley duality, using canonical extensions as an essential tool. Specifically, the theory of canonical extensions…
The theory of natural dualities provides a well-developed framework for studying Stone-like dualities induced by an algebra $\mathbf{L}$ which acts as a dualizing object when equipped with suitable topological and relational structure. The…
We study the relation between augmentations and sheaves in the context of framed oriented links. In this set up, we find slightly more sheaves than augmentations. After removing the sporadic sheaves, we construct a bijective correspondence…
A theory of double affine and special double affine bundles, i.e. differential manifolds with two compatible (special) affine bundle structures, is developed as an affine counterpart of the theory of double vector bundles. The motivation…
It is well known that the variety of Boolean semirings, which is generated by the three element semiring S, is dual to the category of partially Stone spaces. We place this duality in the context of natural dualities. We begin by…
This paper outlines a program in what one might call spectral sheaf theory --- an extension of spectral graph theory to cellular sheaves. By lifting the combinatorial graph Laplacian to the Hodge Laplacian on a cellular sheaf of vector…
We extend Yosida's 1941 version of Stone-Gelfand duality to metrically complete unital lattice-ordered groups that are no longer required to be real vector spaces. This calls for a generalised notion of compact Hausdorff space whose points…
Classic work of Pierce and Dauns-Hofmann shows that biregular rings are dual to simple ring bundles over Stone spaces. We extend this duality to Steinberg rings, a purely algebraic generalisation of Steinberg algebras, and ringoid bundles…