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

The divisors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. To pique the reader’s interest and curiosity let us pose the following riddle: what is an interesting number theoretic characterisation of the… (More)

We use a K-theory recipe of Thomason to obtain classi cations of triangulated subcategories via re ning some standard thick subcategory theorems. We apply this recipe to the full subcategories of… (More)

A ghost over a finite 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 statement that ghosts… (More)

Freyd’s generating hypothesis for the stable module category of a nontrivial finite group G is the statement that a map between finitely generated kGmodules that belongs to the thick subcategory… (More)

The second author fondly remembers how a number of years ago Paulo Ribenboim helped him to escape to the West and immediately upon his arrival welcomed him with beautiful lectures on the Galois group… (More)

Following Krause [Kra99], we prove Krull-Schmidt theorems for thick subcategories of various triangulated categories: derived categories of rings, noetherian stable homotopy categories, stable module… (More)

In this series of lectures we give an exposition of the seminal work of Devinatz, Hopkins, and Smith which is surrounding the classification of the thick subcategories of finite spectra in stable… (More)

In this paper we study wide subcategories. A full subcategory of R-modules is said to be wide if it is abelian and closed under extensions. Hovey [Hov01] gave a classification of wide subcategories… (More)