Author: Mark Hovey
Title: Chromatic phenomena in the algebra of BP_{*}BP-comodules

We describe the author's research with Neil Strickland on the global
algebra and global homological algebra of the category of
$BP_{*}BP$-comodules.  We recall the results of the author and
Strickland, who prove that the category of $E(n)_{*}E(n)$-comodules is a
localization, in the abelian sense, of the category of
$BP_{*}BP$-comodules.  This gives analogues of the usual structure
theorems, such as the Landweber filtration theorem, for
$E(n)_{*}E(n)$-comodules.  We recall the work of the author's paper on
homotopy theory of comodules, where an improved version
$\stable{\Gamma}$ of the derived category of comodules over a
well-behaved Hopf algebroid $(A, \Gamma)$ is constructed.  The main new
result of the paper is that $\stable{E(n)_{*}E(n)}$ is a Bousfield
localization of $\stable{BP_{*}BP}$, in analogy to the abelian case.