Cohomological comparison theorem

An Extension of Tate's Theorem on Cohomological Triviality1

Let G be a finite group and/: A—*B a homomorphism of G-modules. In one form, Tate's theorem says that if, for some r and all subgroups U of G, Êr~liU, f) is a surjection, HriU, f) is an isomorphism, and Hr+1iU, f) is an injection, then HniU, f) is an isomorphism for all U and all ra. Whaples has asked if the modification of this theorem stated below is true, and this paper answers Whaples' ques...

Cohomological Descent

Introduction In classical C̆ech theory, we “compute” (or better: filter) the cohomology of a sheaf when given an open covering. Namely, if X is a topological space, U = {Ui} is an indexed open covering, and F is an abelian sheaf on X, then we get a C̆ech to derived functor spectral sequence E 2 = H (U,H(F ))⇒ H(X,F ), where H(F ) is the presheaf whose value on an open U is H(U,F |U ) (and we use ...

An isoperimetric comparison theorem

Cohomological Bousfield Classes

In this paper, we begin the study of Bousfield classes for cohomology theories defined on spectra. Our main result is that a map f : X → Y induces an isomorphism on E(n)-cohomology if and only if it induces an isomorphism on E(n)-homology. We also prove this for variants of E(n) such as elliptic cohomology and real K-theory. We also show that there is a nontrivial map from a spectrum Z to the K...

The Cohomological Supercharge

We discuss the supersymmetry operator in the cohomological formulation of dimensionally reduced SYM. By establishing the cohomology, a large class of invariants are classified. PACS: 11.25.-w, 12.60.Jv