Related papers: Perfect algebraic stacks
In this paper, the existence of perfect and quasi-perfect splitter sets in finite abelian groups is studied, motivated by their application in coding theory for flash memory storage. For perfect splitter sets we view them as splittings of…
We prove that the dg category of perfect complexes on a smooth, proper Deligne-Mumford stack over a field of characteristic zero is geometric in the sense of Orlov, and in particular smooth and proper. On the level of triangulated…
We give a valuative criterion for when a smooth algebraic stack with a separated good moduli space is the quotient of a separated Deligne-Mumford stack by a torus. For doing so, we introduce a new class of morphisms, the so-called effective…
In combinatorial commutative algebra and algebraic statistics many toric ideals are constructed from graphs. Keeping the categorical structure of graphs in mind we give previous results a more functorial context and generalize them by…
In this paper, we examine the behavior of ideal-adic separatedness and completeness under certain ring extensions using trace map. Then we prove that adic completeness of a base ring is hereditary to its ring extension under reasonable…
The study of Frobenius endomorphism provides numerous information about its corresponding Abelian variety. To understand the action of the Frobenius endomorphism, one may be interested in its eigenvalues. According to Weil's third…
We compactify the moduli stack of maps from curves to certain quotient stacks $\mathcal{X}=[W/G]$ with a projective good moduli space, extending previous results from quasimap theory. For doing so, we introduce a new birational…
Directed spaces are natural topological extensions of dcpos in domain theory and form a cartesian closed category. In order to model nondeterministic semantics, the power structures over directed spaces were defined through the form of free…
A conjecture of Berge suggests that every bridgeless cubic graph can have its edges covered with at most five perfect matchings. Since three perfect matchings suffice only when the graph in question is $3$-edge-colourable, the rest of cubic…
We call a finitely complete category algebraically coherent when the change-of-base functors of its fibration of points are coherent, which means that they preserve finite limits and jointly strongly epimorphic pairs of arrows. We give…
We study torus-equivariant algebraic $K$-theory of affine Schubert varieties in the perfect affine Grassmannians over $\mathbb{F}_p$. We further compare it to the torus-equivariant Hochschild homology of perfect complexes, which has a…
In \cite{CGH15} we introduced TiRS graphs and TiRS frames to create a new natural setting for duals of canonical extensions of lattices. In this continuation of \cite{CGH15} we answer Problem 2 from there by characterising the perfect…
We sketch recent interactions between model theory and a roughly 150-year old study of analytic functions involving complex analysis, algebraic topology, and number theory, centered in canonicity of universal covers. Towards this goal we…
Differential algebraic geometry seeks to extend the results of its algebraic counterpart to objects defined by differential equations. Many notions, such as that of a projective algebraic variety, have close differential analogues but their…
Let $A(G)$ and $B(H)$ be the Fourier and Fourier-Stieltjes algebras of locally compact groups $G$ and $H$, respectively. Ilie and Spronk have shown that continuous piecewise affine maps $\alpha: Y \subseteq H\rightarrow G$ induce completely…
We introduce a commutative associative graded algebra structure on the direct sum Z of the centers of the Hecke algebras associated to the symmetric groups in n letters for all n. As a natural deformation of the classical construction of…
The goal of this paper is to prove that the classifying spaces of categories of algebras governed by a prop can be determined by using function spaces on the category of props. We first consider a function space of props to define the…
We give a definition of twisted map to a quotient stack with projective good moduli space, and we show that the resulting functor satisfies the existence part of the valuative criterion for properness.
Let $k$ be a field. We characterize the group schemes $G$ over $k$, not necessarily affine, such that $\mathsf{D}_{\mathrm{qc}}(B_kG)$ is compactly generated. We also describe the algebraic stacks that have finite cohomological dimension in…
In this article we investigate the notion and basic properties of Boolean algebras and prove the Stone's representation theorem. The relations of Boolean algebras to logic and to set theory will be studied and, in particular, a neat proof…