Let k be an algebraically closed field of characteristic p. We shall discuss the cohomology algebras of a block ideal B of the group algebra kG of a finite group G and a block ideal C of the block ideal of kH of a subgroup H of G which are in Brauer correspondence and have a common defect group, continuing [4]. We shall define a (B,C)-bimodule L. The k-dual L∗ induces the transfer map between t...

In this note we describe aspects of the cohomology of coherent sheaves on a complete toric variety X over a field k and, more generally, the local cohomology, with supports in a monomial ideal, of a finitely generated module over a polynomial ring S. This leads to an efficient way of computing such cohomology, for which we give explicit algorithms. The problem is finiteness. The ith local cohom...

Let p be an odd prime number and let S be a finite set of prime numbers congruent to 1 modulo p. We prove that the group GS(Q)(p) has cohomological dimension 2 if the linking diagram attached to S and p satisfies a certain technical condition, and we show that GS(Q)(p) is a duality group in these cases. Furthermore, we investigate the decomposition behaviour of primes in the extension QS(p)/Q a...

‎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...

in this paper we introduce a new definition of the first non-abelian cohomology of topological groups.  we relate the cohomology of a normal subgroup $n$ of a topological group $g$ and the quotient $g/n$ to the cohomology of $g$. we get the inflation-restriction exact sequence. also, we obtain a seven-term exact cohomology sequence up to dimension 2. we give an interpretation of the first non-a...

A general structure theorem on higher order invariants is proven. For an arithmetic group, the structure of the corresponding Hecke module is determined. It is shown that the module does not contain any irreducible submodule. This explains the fact that L-functions of higher order forms have no Euler-product. Higher order cohomology is introduced, classical results of Borel are generalized and ...

We introduced a braided Sweedler cohomology, which is adequate to work with the H-braided cleft extensions studied in [G-G1]. Introduction In [Sw] a cohomology theory H(H,A) for a commutative module algebra A over a cocommutative Hopf algebra H was introduced. This cohomology is related to those of groups an Lie algebras in the following sense. When H is a group algebra k[G], then H(H,A) is can...

Let (R,m) be a local Noetherian ring, let I ⊂ R be any ideal and let M be a finitely generated R-module. It has been long conjectured that the local cohomology modules H I(M) have finitely many associated primes for all i (see Conjecture 5.1 in [H] and [L].) If R is not required to be local these sets of associated primes may be infinite, as shown by Anurag Singh in [S], where he constructed an...

Let Γ be the mapping class group of an oriented surface Σ of genus g with r boundary components. We prove that the first cohomology group H(Γ,O(MSL2(C)) ∗) is non-trivial, where the coefficient module is the dual of the space of algebraic functions on the SL2(C) moduli space over Σ.