I know of two very general frameworks for describing generalizations of what a "cohomology theory" should be: Grothendieck's "six functors", and the theory of spectra. In the former, one assigns to ...
Does Wolbert's derived equivalence between $E_*^R$-local $R$-modules and $R_E$-modules come from a Quillen equivalence?
Let $R$ be a ring spectrum (in the world of EKMM $S$-modules) and let $E$ be a smashing $R$-module. Denote by $R_E$ the $E_*$-localization of $R$. By a theorem of Wolbert (Theorem 2 in Classifying ...
This should be obvious but I'm not seeing it: The $\mathfrak T$ be a triangulated category with coproducts and with a compact generator $A$ (that is, the functor $\mathfrak T(A,\_)$ preserves ...
For a derived category of a Noetherian ring (or perhaps more generally), can we talk about a Periodicity Theorem? We have Thick Subcategory Theorems and Nilpotence Theorems (HPS 91) for D(R), and in ...