Related papers: Finitistic Dimension Conjecture and Conditions on …
We continue our study of F-thresholds begun in math/0607660 by an in depth analysis of the hypersurface case. We use the D--module theoretic description of generalized test ideals which allows us to show that in any F--finite regular ring…
We study the existence of maximal ideals in preadditive categories defining an order $\preceq$ between objects, in such a way that if there do not exist maximal objects with respect to $\preceq$, then there is no maximal ideal in the…
We introduce Igsua-Todorov distances of Artin algebra, prove its invariance under derived equivalence, present its application to exterior algebra, and establish the link between the dimension of the singularity category and this distance.
The finitistic dimension conjecture is closely connected to the symmetry of the finitistic dimension. Recent work indicates that such connection extends to one of its upper bounds, the delooping level. In this paper, we show that the same…
Ideals of continuous functions which satisfy an off diagonality condition proved to be important connected with the solution of large classes of nonlinear PDEs, and more recently, in General Relativity and Quantum Gravity. Maximal ideals…
We investigate two invariants of Noetherian semiperfect rings, namely the depth and a new invariant we call the "delooping level". These give lower and upper bounds for the finitistic dimension, respectively. As first theorems, we give a…
Extension conjecture states that if a simple module over an artin algebra has nonzero first self-extension group then it has nonzero i-th self-extension group for infinitely many positive integers i. It is shown by recollement of…
Let R be a regular ring of characteristic p. Hochster showed that the category of Lyubeznik's F-modules has enough injectives, so that every F-module has an injective resolution in this category. We show that under mild conditions on R, for…
In these notes we will survey recent results on various finitary approximation properties of infinite groups. We will discuss various restrictions on groups that are approximated for example by finite solvable groups or finite-dimensional…
We combine two of Igusa's conjectures with recent semi-continuity results by Musta\c{t}\u{a} and Popa to form a new, natural conjecture about bounds for exponential sums. These bounds have a deceivingly simple and general formulation in…
New homotopy invariant finiteness conditions on modules over commutative rings are introduced, and their properties are studied systematically. A number of finiteness results for classical homological invariants like flat dimension,…
Our purpose in this work is multifold. First, we provide general criteria for the finiteness of the projective and injective dimensions of a finite module $M$ over a (commutative) Noetherian ring $R$. Second, in the other direction, we…
We provide algebraic conditions ensuring the decidability of the theory of modules over effectively given Pr\"ufer (in particular B\'ezout) domains whose localizations at maximal ideals have dense value groups. For B\'ezout domains, these…
The tensor ideal localising subcategories of the stable module category of all, including infinite dimensional, representations of a finite group scheme over a field of positive characteristic are classified. Various applications concerning…
Let $A$ be an Artin algebra. We investigate subalgebras of $A$ with certain conditions and obtain some classes of algebras whose finitistic dimensions are finite.
In this note by using elementary considerations, we settle Fr\"oberg's conjecture for a large number of cases, when all generators of ideals have the same degree.
We consider the question of whether the injective modules generate the unbounded derived category of a ring as a triangulated category with arbitrary coproducts. We give an example of a non-Noetherian commutative ring where they don't, but…
The paper concerns the study of new classes of nonlinear and nonconvex optimization problems of the so-called infinite programming that are generally defined on infinite-dimensional spaces of decision variables and contain infinitely many…
We consider deformations of bounded complexes of modules for a profinite group G over a field of positive characteristic. We prove a finiteness theorem which provides some sufficient conditions for the versal deformation of such a complex…
We provide a generalization of first-order necessary conditions of optimality for infinite-dimensional optimization problems with a finite number of inequality constraints and with a finite number of inequality and equality constraints. Our…