‎we introduce a generalization of the notion of‎ depth of an ideal on a module by applying the concept of‎ local cohomology modules with respect to a pair‎ ‎of ideals‎. ‎we also introduce the concept of $(i,j)$-cohen--macaulay modules as a generalization of concept of cohen--macaulay modules‎. ‎these kind of modules are different from cohen--macaulay modules‎, as an example shows‎. ‎also an art...

This is an introductory survey of the theory of p-form conservation laws in field theory. It is based upon a series of lectures given at the Second Mexican School on Gravitation and In these lectures I will provide a survey of some aspects of the theory of local coho-mology in field theory and provide some illustrative applications, primarily taken from the Einstein equations of the general the...

HOMOTOPY THEORY AND GENERALIZED SHEAF COHOMOLOGY BY KENNETHS. BROWN0) ABSTRACT. Cohomology groups Ha(X, E) are defined, where X is a topological space and £ is a sheaf on X with values in Kan's category of spectra. These groups generalize the ordinary cohomology groups of X with coefficients in an abelian sheaf, as well as the generalized cohomology of X in the usual sense. The groups are defin...

We propose a new point of view of the Spencer cohomology appearing in the formal theory of differential equations based on a dual approach via comodules. It allows us to relate the Spencer cohomology with standard constructions in homological algebra and, in particular, to express it as a Cotor. We discuss concrete methods for its construction based on homological perturbation theory. Appears i...

A cohomology theory of weighted Rota-Baxter $3$-Lie algebras is introduced. Formal deformations, abelian extensions, skeletal 2-algebras and crossed modules 3-Lie are interpreted by using lower degree groups.

In this paper, we introduce the cohomology theory of O -operators on Hom-associative algebras. This can also be viewed as Hochschild a certain algebra with coefficients in suitable bimodule. Next, study infinitesimal and formal deformations an -operator show that they are governed by above-defined cohomology. Furthermore, notion Nijenhuis elements associated is introduced to characterize trivia...

Background Cohomological descent is a robust computational and theoretical tool, central to p-adic cohomology and its applications. On the one hand, it facilitates explicit calculations (analogous to the computation of coherent cohomology in scheme theory via Čech cohomology); on the other, it allows one to deduce results about singular schemes (e.g., finiteness of the cohomology of overconverg...