In terms of generators and defining relations, a description is given of the Hochschild cohomology algebra for one of the series of local algebras of quaternion type. As a corollary, the Hochschild cohomology algebra is described for the group algebras of generalized quaternion groups over algebraically closed fields of characteristic 2. Introduction Let R be a finite-dimensional algebra over a...

where the map R/(x1 , . . . , x m n ) −→ R/(x m+1 1 , . . . , x m+1 n ) is multiplication by the image of the element x1 · · ·xn. As these descriptions suggest, H a(R) is usually not finitely generated as an R-module. However local cohomology modules have useful finiteness properties in certain cases, e.g., for a local ring (R,m), the modules H m(R) satisfy the descending chain condition. This ...

In this paper, considering the difference between the finiteness dimension and cohomological dimension for a finitely generated module, we investigate the asymptotic behavior of grades of components of graded local cohomology modules with respect to irrelevant ideal; as long as we study some artinian and tameness property of such modules.

We continue studying the class of modules having reducible complexity over a local ring. In particular, a method is provided for computing an upper bound of the complexity of such a module, in terms of vanishing of certain cohomology modules. We then specialize to complete intersections, which are precisely the rings over which all modules have finite complexity.

A method is provided for computing an upper bound of the complexity of a module over a local ring, in terms of vanishing of certain cohomology modules. We then specialize to complete intersections, which are precisely the rings over which all modules have finite complexity.

Let R be a d-dimensional local ring, with maximal ideal m, containing a field and let x1, . . . , xd be a system of parameters for R. If depthR ≥ d − 1 and the local cohomology module H m (R) is finitely generated, then there exists an integer n such that the modules R/(x 1 , . . . , x d ) have the same Betti numbers, for all i ≥ n.

Abstract We employ the inductive structure of determinantal varieties to calculate mixed Hodge module local cohomology modules with support. show that weight a simple composition factor is uniquely determined by its support and cohomological degree. As consequence, we obtain equivariant filtration on each module. Finally, as an application, provide formula for generation level these modules.

We study the algebraic Gauss-Manin system and the algebraic Brieskorn module associated to a polynomial mapping with isolated singularities. Since the algebraic GaussManin system does not contain any information on the cohomology of singular fibers, we first construct a non quasi-coherent sheaf which gives the cohomology of every fiber. Then we study the algebraic Brieskorn module, and show tha...

The Hom closed colocalizing subcategories of the stable module category of a finite group are classified. Along the way, the colocalizing subcategories of the homotopy category of injectives over an exterior algebra, and the derived category of a formal commutative differential graded algebra, are classified. To this end, and with an eye towards future applications, a notion of local homology a...

The present paper can be considered as a natural extension the article [Ar7]. Fix root data (Y,X, . . . ) of the finite type (I, ·) and a positive integer number l. In [Ar7] we obtained a nice description for semiinfinite cohomology of the trivial module C over the small quantum group ul corresponding to the root data (Y,X, . . . ) in terms of local cohomology of the structure sheaf on the nilp...