We compute the 5-local cohomology of a particular Hopf algebroid related to algebraic topology and algebraic geometry. This computation arises in a number of settings, and it is a 5-local analogue of the Weierstrass Hopf algebroid used to compute tmf homology. We finish the paper by computing Adams-Novikov differentials in the cohomology, giving the homotopy, V (0)homology, and V (1)-homology o...

Let I denote an ideal of a local Gorenstein ring (R, m). Then we show that the local cohomology module H I (R), c = height I, is indecomposable if and only if V (Id) is connected in codimension one. Here Id denotes the intersection of the highest dimensional primary components of I. This is a partial extension of a result shown by Hochster and Huneke in the case I the maximal ideal. Moreover th...

We apply constructions from equivariant topology to Benson-Carlson resolutions and hence prove in (2.1) that the group cohomology ring of a nite group enjoys remarkable duality properties based on its global geometry. This recovers and generalizes the result of Benson-Carlson stating that a Cohen-Macaulay cohomology ring is automatically Gorenstein. We give an alternative approach to Tate cohom...

We show how the classical notions of cohomology with local coefficients, CW-complex, covering space, homeomorphism equivalence, simple homotopy tubular neighbourhood, and spinning can be encoded on a computer used to calculate ambient isotopy invariants continuous embeddings N ↪ M one topological manifold into another. More specifically, we describe an algorithm for computing homology H n ( X ,...

Let f be a degeneration of Kähler manifolds. The local invariant cycle theorem states that for a smooth fiber of the degeneration, any cohomology class, invariant under the monodromy action, rises from a global cohomology class. Instead of the classical cohomology, one may consider the non-abelian cohomology. This note demonstrates that the analogous non-abelian version of the local invariant c...