The Orlov spectrum is a new invariant of a triangulated category. It was introduced by D.
Orlov, building on work of A. Bondal-M. Van den Bergh and R. Rouquier. The supremum of …

We study modules over the commutative ring spectrum HF2^ HF2, whose coefficient groups
are quotients of the dual Steenrod algebra by collections of the Milnor generators. We show …

Freyd's generating hypothesis, interpreted in the stable module category of a finite p-group
G, is the statement that a map between finite-dimensional kG-modules factors through a …

We show that a strong form (the fully faithful version) of the generating hypothesis,
introduced by Freyd in algebraic topology, holds in the derived category of a ring R if and …

A ghost over a finite p-group G is a map between modular representations of G which is
invisible in Tate cohomology. Motivated by the failure of the generating hypothesis—the …

Freyd's generating hypothesis for the stable module category of a non-trivial finite group $ G
$ is the statement that a map between finitely generated $ kG $-modules that belongs to the …

A ghost in the stable module category of a group $ G $ is a map between representations of
$ G $ that is invisible to Tate cohomology. We show that the only non-trivial finite $ p …

Let A be a finite connected graded cocommutative Hopf algebra over a field k. There is an
endofunctor tw on the stable module category StMod A of A which twists the grading by 1 …

Freyd's generating hypothesis in stable homotopy theory is revisited and new consequences
and equivalent forms of it are derived. A surprising such consequence is that I, the Brown …

We define global dimension and weak dimension for the structured ring spectra that arise in
algebraic topology. We provide a partial classification of ring spectra of global dimension …