Related papers: Cross effects for functors from posets
Quasi-projective dimension of modules over associative rings is generalized in this paper to the one of complexes of modules. Basic properties of this dimension are established, including a comparison result with projective dimension and a…
Projectively coresolved Gorenstein flat modules were introduced recently by Saroch and Stovicek and were shown to be Gorenstein projective. While the relation between Gorenstein projective and Gorenstein flat modules is not well understood,…
Given a functor from any category into the category of topological spaces, one obtains a linear representation of the category by post-composing the given functor with a homology functor with field coefficients. This construction is…
Let R be a complete intersection ring and let M and N be R-modules. It is shown that the vanishing of Ext^i_R(M,N) for a certain number of consecutive values of i starting at n forces the complete intersection dimension of M to be at most…
This work present a new class of variational wave functions for fermi systems in any dimension. These wave functions introduce correlations between Cooper pairs in different momentum states and the relevant correlations can be computed…
We prove inequalities relating the absolute value of the determinant of n+1 linearly independent unit vectors in an n+1 dimensional complex vector space and the projective distances from the vertices to the hyperplanes containing the…
A correspondence functor is a functor from the category of finite sets and correspondences to the category of $k$-modules, where $k$ is a commutative ring. We determine exactly which simple correspondence functors are projective. Moreover,…
We explore the interlacing between model category structures attained to classes of modules of finite $\mathcal{X}$-dimension, for certain classes of modules $\mathcal{X}$. As an application we give a model structure approach to the…
We investigate the representation theory of finite sets. The correspondence functors are the functors from the category of finite sets and correspondences to the category of k-modules, where k is a commutative ring. They have various…
We determine a family of functors from a poset to abelian groups such that the higher direct limits vanish on them. This is done by first characterizing the projective functors. Then a spectral sequence arising from the grading of the poset…
The category of small covariant functors from simplicial sets to simplicial sets supports the projective model structure. In this paper we construct various localizations of the projective model structure and also give a variant for…
A multiplication on persistence diagrams is introduced by means of Schubert calculus. The key observation behind this multiplication comes from the fact that the representation space of persistence modules has the structure of the Schubert…
We study the relationship between Iitaka fibrations and the conjecture on the existence of complements, assuming the good minimal model conjecture. In one direction, we show that the conjecture on the existence of complements implies the…
This survey discusses hyperbolicity properties of moduli stacks and generalisations of the Shafarevich Hyperbolicity Conjecture to higher dimensions. It concentrates on methods and results that relate moduli theory with recent progress in…
We develop a new technique for computing higher limits of functors over filtered posets by constructing explicit fibrant replacements within a suitable model category structure. We apply this procedure to develop two systematic vanishing…
We introduce separable functors of the second kind (or $H$-separable functors) and $H$-Maschke functors. $H$-separable functors are generalizations of separable functors. Various necessary and sufficient conditions for a functor to be…
We present the shift-dimension of multipersistence modules and investigate its algebraic properties. This gives rise to a new invariant of multigraded modules over the multivariate polynomial ring arising from the hierarchical stabilization…
From certain triangle functors, called non-negative functors, between the bounded derived categories of abelian categories with enough projective objects, we introduce their stable functors which are certain additive functors between the…
We consider relative Tor functors built from resolutions described by a semidualizing module C over a commutative noetherian ring R. We show that the bifunctors Tor^{F_CM}_i (-,-) and Tor^{P_CM}_i (-,-), defined using flat-like and…
Derived functors (or Zuckerman functors) play a very important role in the study of unitary representations of real reductive groups. These functors are usually applied on highest weight modules in the so-called good range and the theory is…