Related papers: Dualizing and canonical complexes on finite posets

Poset-theoretic generalizations of set-theoretic committee constructions are presented. The structure of the corresponding subposets is described. Sequences of irreducible fractions associated to the principal order ideals of finite bounded…

We use Grothendieck theorem to prove a structure theorem for multicorrelation sequences of length two, associated with two (not necessarily commuting) measure preserving actions on a probability space. We use this to deduce a multiple…

In this article we extend Deligne's construction of Grothendieck's six operations on the derived category of torsion sheaves over the \'etale site of a scheme for morphisms of finite type to a larger class of morphisms. This class includes…

Motivated by the classical type decomposition of von Neumann algebras, and various more recent extensions to other structures, we develop a type decomposition theory for general posets.

Monadic second order logic is the expansion of first order logic by quantifiers ranging over unary relations. We study the shared monadic second order theory of finite linear orders, i.e. the pseudofinite monadic second order theory of…

We give a new proof of a recent result due to Mats Andersson and Elizabeth Wulcan, generalizing the local Grothendieck duality theorem. It can also be seen as a generalization of a previous result by Mikael Passare. Our method does not…

Separation systems are posets with additional structure that form an abstract setting in which tangle-like clusters in graphs, matroids and other combinatorial structures can be expressed and studied. This paper offers some basic theory…

We show a variation of the usual homological freeness criterion for operadic modules over a Koszul operad. We then apply this result to decorated partition posets for some operads, showing that their augmentation is Cohen-Macaulay and…

We apply the homomorphism complex construction to partially ordered sets, introducing a new topological construction based on the set of maximal chains in a graded poset. Our primary objects of study are distributive lattices, with special…

In Commutative Algebra structure results on minimal free resolutions of Gorenstein modules are of classical interest. We define Gorenstein modules of finite length over the weighted polynomial ring via symmetric matrices in divided powers.…

In this paper we use recently developed calculus of residue currents together with integral formulas to give a new explicit analytic realization, as well as a new analytic proof of Serre duality on any reduced pure $n$-dimensional…

We define a poset of partitions associated to an operad. We prove that the operad is Koszul if and only if the poset is Cohen-Macaulay. In one hand, this characterisation allows us to compute the homology of the poset. This homology is…

This is both an expository and research paper where we advocate a systematic study of continuous analogues of finite partially ordered sets, convex polytopes, oriented matroids, arrangements of subspaces, finite simplicial complexes, and…

We present a method to compute integral cohomology of posets. This toolbox is applicable as soon as the sub-posets under each object possess certain structure. This is the case for simplicial complexes and simplex-like posets. The method is…

We study consequences and applications of the folklore statement that every double complex over a field decomposes into so-called squares and zigzags. This result makes questions about the associated cohomology groups and spectral sequences…

In this paper we study finite Eulerian posets which are binomial, Sheffer or triangular. These important classes of posets are related to the theory of generating functions and to geometry. The results of this paper are organized as…

We give a classification of all exact structures on a given idempotent complete additive category. Using this, we investigate the structure of an exact category with finitely many indecomposables. We show that the relation of the…

We introduce a notion of proper morphism for schematic finite spaces and prove the analogue of Grothendieck's finiteness theorem for it by means of the classic result for schemes and general descent arguments. This result also generalizes…

We introduce a class of proper posets which is preserved under countable support iterations, includes $\omega^\omega$-bounding, Cohen, Miller, and Mathias posets associated to filters with the Hurewicz covering properties, and has the…

We prove basic facts about reflexivity in derived categories over noetherian schemes; and about related notions such as semidualizing complexes, invertible complexes, and Gorenstein-perfect maps. Also, we study a notion of rigidity with…