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 …

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 …

In this note, we give a brief overview of the telescope conjecture and the chromatic splitting
conjecture in stable homotopy theory. In particular, we provide a proof of the folklore result …

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 …

A theory of ordinal powers of the ideal $\mathfrak {g} _ {\mathcal {S}} $ of $\mathcal {S} $-
ghost morphisms is developed by introducing for every ordinal $\lambda $, the $\lambda …

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 …

Motivated by Freyd's famous unsolved problem in stable homotopy theory, the generating
hypothesis for the stable module category of a finite group is the statement that if a map in …

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 …

Let G be a finite group, and let k be a field whose characteristic p divides the order of G.
Freyd's generating hypothesis for the stable module category of G is the statement that a …