Related papers: Finitistic Dimension Conjecture and Conditions on …

We produce a criterion for open sets in projective $n$-space over a separably closed field to have \'etale cohomological dimension bounded by $2n-3$. We use the criterion to exhibit a scheme for which \'etale cohomological dimension is…

Higher dimensional generalisations of self-duality conditions and of theta angle terms are analysed in Yang-Mills theories. For the theory on a torus, the torus metric and various antisymmetric tensors are viewed as coupling constants…

The Brauer-Thrall Conjectures, now theorems, were originally stated for finitely generated modules over a finite-dimensional $\sk$-algebra. They say, roughly speaking, that infinite representation type implies the existence of lots of…

This paper explores the solution of Fredholm-like equations with infinite dimensional solution spaces. We set out to find a method for determining a particular solution to a Fredholm-like equation subject to a given constraint. The…

For a fusion category, we prove some new integral properties concerning the dimension of a simple object that generates a Isaacs fusion subcategory. A stronger divisibility result is proven for any modular fusion category. This divisibility…

We introduce and study a special class of ideals, called tropical ideals, in the semiring of tropical polynomials, with the goal of developing a useful and solid algebraic foundation for tropical geometry. The class of tropical ideals…

We introduce a generalization of tilting modules of finite projective dimension, projectively Wakamatsu tilting modules, which are self-orthogonal and Ext-progenerators in their Ext-perpendicular categories. Under a certain finiteness…

This paper provides the theory of integration with respect to Euler characteristics of finite categories. As an application, we use sensors to enumerate the targets lying on a poset. This is a discrete analogue to Baryshnikov and Ghrist's…

We study problems related to indecomposability of modules over certain local finite dimensional trivial extension algebras. We do this by purely combinatorial methods. We introduce the concepts of graph of cyclic modules, of combinatorial…

The structures of the ideals of Clifford algebras which can be both infinite dimensional and degenerate over the real numbers are investigated.

We prove an upper bound on the log canonical threshold of a hypersurface that satisfies a certain power condition and use it to prove several generalizations of Igusa's conjecture on exponential sums, with the log-canonical threshold in the…

In this work, we extend the concept of the double of an ideal defined in \cite{G2}, to the context of modules. We also obtain the genericity of the infinitesimal Lipschitz condition A for an enlarged class of analytic spaces.

We consider ideals arising in the context of conditional independence models that generalize the class of ideals considered by Fink [7] in a way distinct from the generalizations of Herzog-Hibi-Hreinsdottir-Kahle-Rauh [13] and Ay-Rauh [1].…

We translate notions and results of decomposition and dimension theories for module categories, into the lattice environment. In particular we translate dimension theory in module categories to complete modular upper-continuous lattices.

We characterize the corings whose category of comodules has a generating set of small projective comodules in terms of the (non commutative) descent theory. In order to extricate the structure of these corings, we give a generalization of…

Matrix conditions extend linear Mal'tsev conditions from Universal Algebra to exactness properties in Category Theory. Some can be stated in the finitely complete context while, in general, they can only be stated for regular categories. We…

This paper deals with the notion of grade of ideals with respect to torsion theories defined via some homological tools such as Ext-modules, Koszul cohomology modules, \v{C}ech and local cohomology modules over commutative rings which are…

In this paper we investigate three unsolved conjectures in geometric combinatorics, namely Falconer's distance set conjecture, the dimension of Furstenburg sets, and Erdos's ring conjecture. We formulate natural $\delta$-discretized…

The aim of this paper is to refine and extend proposals by Sozeau and Tabareau and by Voevodsky for universe polymorphism in type theory. In those systems judgments can depend on explicit constraints between universe levels. We here present…

The exterior degree of a finite group has been introduced in [P. Niroomand and R. Rezaei, On the exterior degree of finite groups, Comm. Algebra 39 (2011), 335--343] and the present paper is devoted to study the exterior degree of infinite…