Related papers: Baker-Beynon duality beyond semisimplicity

In this paper we develop a duality theory for all finite-dimensional near-vector spaces and introduce a notion of inner product tailored to the broad and natural class of strongly regular near-vector spaces. This generalized construction…

Applying a general categorical construction for the extension of dualities, we present a new proof of the Fedorchuk duality between the category of compact Hausdorff spaces with their quasi-open mappings and the category of complete normal…

We propose a family of IR dualities for 3d $\mathcal{N}=4$ $U(N)$ SQCD with $N_f$ fundamental flavors and $P$ Abelian hypermultiplets i.e. $P$ hypermultiplets in the determinant representation of the gauge group. These theories are good in…

Through the notion of weakly sound class of weights, we recover many known dualities involving accessible categories with a chosen class of limits, as instances of a general duality theorem. These include the Gabriel-Ulmer duality for…

We propose a description of T-duality between general geometric and non-geometric backgrounds as higher groupoid bundles with connections. Our description extends the previous observation by Nikolaus and Waldorf that the topological aspects…

This monograph develops the theory of Besov spaces for abelian group actions on semifinite von Neumann algebras and then proves Peller criteria for traceclass properties of associated Hankel operators. This allows to extend known index…

Let A be an abelian variety over a number field K. An identity between the L-functions L(A/K_i,s) for extensions K_i of K induces a conjectural relation between the Birch-Swinnerton-Dyer quotients. We prove these relations modulo finiteness…

Suppose that we have a bicomplete closed symmetric monoidal quasi-abelian category $\mathcal{E}$ with enough flat projectives, such as the category of complete bornological spaces $\textbf{CBorn}_k$ or the category of inductive limits of…

This note is a sequel to Shu-Xue-Yao's paper \cite{BYY} where the author studied the so-called enhanced groups and related dualities for type $A$. In this note, we continue to investigate the enhanced dualities for classical groups of type…

We study the link between a compact hypersurface in $\P^{n+1}$ and the set of all its tangent planes. In this context, we identify $\P^{n+1}$ to the set of linear subspaces of codimension one by orthogonal complementarity. This gives rise…

For a large class of Abelian lattice models with sign problems, including the case of non-zero chemical potential, duality maps models with complex actions into dual models with real actions. For extended regions of parameter space,…

We study the analytic and topological invariants associated with complex normal surface singularities. Our goal is to provide topological formulae for several discrete analytic invariants whenever the analytic structure is generic (with…

We interpret the structure of the adele class space of the rationals--and specifically its Riemann sector--as the natural monoidal extension of the Picard group of the arithmetic curve $\overline{\operatorname{Spec} \mathbb Z}$. We identify…

We use the exterior product of double forms to reformulate celebrated classical results of linear algebra about matrices and bilinear forms namely the Cayley-Hamilton theorem, Laplace expansion of the determinant, Newton identities and…

In a previous paper, the authors defined an equivariant version of the so-called Saito duality between the monodromy zeta functions as a sort of Fourier transform between the Burnside rings of an abelian group and of its group of…

We classify the enhanced helicity symmetry of the Ehlers group to extended supergravity theories in any dimension. The vanishing character of the pseudo-Riemannian cosets occurring in this analysis is explained in terms of Poincar\'e…

The goal of this thesis is to define a 2-dimensional version of abelian categories, where symmetric 2-groups play the role that abelian groups played in 1-dimensional algebra. Abelian and 2-abelian groupoid enriched categories are defined…

This is the first in a series of papers that deals with duality statements such as Mukai-duality (T-duality, from algebraic geometry) and the Baum-Connes conjecture (from operator $K$-theory). These dualities are expressed in terms of…

Let $X$ be a Banach space. Then $X$ is complemented in the bidual $X^{**}$ if and only if there exists an invariant mean $\ell_\infty(G, X)\to X$ with respect to a free Abelian group $G$ of rank equal to the cardinality of $X^{**}$, and…

We present a robust categorical foundation for the duality theory introduced by Eisenbud and Schreyer to prove the Boij-S\"oderberg conjectures describing numerical invariants of syzygies. The new foundation allows us to extend the reach of…