Related papers: Cubical sites as Eilenberg-Zilber categories

Using the classical universal coefficient theorem of Rosenberg-Schochet, we prove a simple classification of all localizing subcategories of the Bootstrap category of separable complex C*-algebras. Namely, they are in bijective…

Constellations are partial algebras that are one-sided generalisations of categories. It has previously been shown that the category of inductive constellations is isomorphic to the category of left restriction semigroups. Here we consider…

We prove that Kellendonk's $C^*$-algebra of an aperiodic and repetitive tiling with finite local complexity is classifiable by the Elliott invariant. Our result follows from showing that tiling $C^*$-algebras are $\mathcal{Z}$-stable, and…

We prove the following theorems: Theorem 1: For any E-field with cyclic kernel, in particular $\mathbb C$ or the Zilber fields, all real abelian algebraic numbers are pointwise definable. Theorem 2: For the Zilber fields, the only pointwise…

Many special classes of simplicial sets, such as the nerves of categories or groupoids, the 2-Segal sets of Dyckerhoff and Kapranov, and the (discrete) decomposition spaces of G\'{a}lvez, Kock, and Tonks, are characterized by the property…

By the result of Artin--Tate--Van den Bergh, every $3$-dimensional cubic AS-regular algebra A can be expressed as a geometric algebra $A=\mathcal{A}(E,\sigma)$, where $E$ is either $\mathbb{P}^{1}\times \mathbb{P}^{1}$ or a curve of…

Strongly $\mathbb{Z}$-graded algebras or principal circle bundles and associated line bundles or invertible bimodules over a class of generalized Weyl algebras $\mathcal{B}(p;q, 0)$ (over a ring of polynomials in one variable) are…

Assume that a basic algebra $A$ over an algebraically closed field $\Bbbk$ with a basic set $A_0$ of primitive idempotents has the property that $eAe=\Bbbk$ for all $e \in A_0$. Let $n$ be a nonzero integer, and $\phi$ and $\psi$ two…

We are concerned with finding explicit generators of the Brauer group of diagonal cubic surfaces in terms of norm residue symbols, which was originally studied by Manin. We introduce the notion of uniform generators and find that the Brauer…

We say that a Riemannian manifold M has rank at least k if every geodesic in M admits at least k parallel Jacobi fields. The Rank Rigidity Theorem of Ballmann and Burns-Spatzier, later generalized by Eberlein-Heber, states that a complete,…

The main goal of this note is to suggest an algebraic approach to the quasi-isometric classification of partially commutative groups (alias right-angled Artin groups). More precisely, we conjecture that if the partially commutative groups…

We develop a new approach to the classical problem on isotopy classification of embeddings of manifolds into Euclidean spaces. This approach involves studying of a new embedding invariant, of almost-embeddings and of smoothing, as well as…

We formulate two conjectures about etale cohomology and fundamental groups motivated by categoricity conjectures in model theory. One conjecture says that there is a unique Z-form of the etale cohomology of complex algebraic varieties, up…

In 2009, Keller and Yang categorified quiver mutation by interpreting it in terms of equivalences between derived categories. Their approach was based on Ginzburg's Calabi-Yau algebras and on Derksen-Weyman-Zelevinsky's mutation of quivers…

In his proof of the K(pi,1) conjecture for complex reflection arrangements, Bessis defined Garside categories suitable for studying braid groups of centralizers of Springer regular elements in well-generated complex reflection groups. We…

We prove a categorical version of the Torelli theorem for cubic threefolds. More precisely, we show that the non-trivial part of a semi-orthogonal decomposition of the derived category of a cubic threefold characterizes its isomorphism…

We show that for certain class of oligomorphic groups there is a version of multiplication of double cosets in the Ismagilov--Olshanski sense. Categories of (reduced) double cosets are realized as certain categories of partial bijections.…

Let $E$ be a Koszul Frobenius algebra. A Clifford deformation of $E$ is a finite dimensional $\mathbb Z_2$-graded algebra $E(\theta)$, which corresponds to a noncommutative quadric hypersurface $E^!/(z)$, for some central regular element…

From the structure of the category of representations of an affine cycle-free quiver, we determine an explicit linear form on the space of regular cuspidal functions over a finite field: its kernel is exactly the space of cuspidal…

Zauner's conjecture concerns the existence of $d^2$ equiangular lines in $\mathbb{C}^d$; such a system of lines is known as a SIC. In this paper, we construct infinitely many new SICs over finite fields. While all previously known SICs…