Topologists and algebraists have been independently studying the homotopy category for a
long time. To a large extent the theories they have developed are parallel. But the …

4.1. Preliminaries 4.2. Vanishing lines 4.3. Morava K-theories and the Adams spectral
sequence 4.4. Examples of self maps 4.5. Proof that Theorem 7 implies Theorem 2 5 …

We define and investigate a class of categories with formal properties similar to those of the
homotopy category of spectra. This class includes suitable versions of the derived category …

Nilpotence and Periodicity in Stable Homotopy Theory describes some major advances
made in algebraic topology in recent years, centering on the nilpotence and periodicity …

Following the conventions of algebraists, we will call triangulated subcategories of D*(R)
epaisse if they are full and closed under direct summands. Hopkins' theorem is a beautiful …

We define the spectrum of a tensor triangulated category as the set of so-called prime ideals,
endowed with a suitable topology. In this very generality, the spectrum is the universal space …

The first main result of this paper is a bijective correspondence between the strictly full
triangulated subcategories dense in a given triangulated category and the subgroups of its …

In the course of his work on the J homomorphism [1] Adams produced for each prime pa self-
map a:* PMP Mp of the mod (p) Moore spectrum. Here kp= 2p-2 if p is odd while k2= 8, and …

In this monograph we give an exposition of some recent development in homotopy theory. It
relates to advances in periodicity in homotopy localization and in cellular spaces. The notion …

It is possible to associate a topological space to the category of modules over any ring. This
space, the Ziegler spectrum, is based on the indecomposable pure-injective modules …