2003/01/21 by Mark Hovey, Hovey, Mark
Computer Science · Mathematics · #55N22 #Advanced Algebra and Logic #Algebraic Topology (math.AT) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras #math.AT #msc:55N22
paper · pdf · doi:10.48550/arxiv.math/0301230
30 pages
arxiv created 2003/01/21 · openalex publication_date 2003/01/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper begins with an exposition of the author's research on the category of BP_*BP-comodules, much of which is joint with Neil Strickland. The main result of that work is that the category of E(n)_*E(n)-comodules is equivalent to a localization of the category of BP_*BP-comodules (the localization is Ln, analogous to the topological Ln). The main new result in this paper is that, analogously, the stable homotopy category of E(n)_*E(n)-comodules is equivalent to a localization (the finite localization Lnf this time, not Ln) of the stable homotopy category of BP_*BP-comodules. These stable homotopy categories were constructed in previous work of the author, and are supposed to model stable homotopy theory; it is like stable homotopy theory where there are no differentials in the Adams-Novikov spectral sequence. Our result embeds the Miller-Ravenel and Hovey-Sadofsky change of rings theorems as special cases of more general isomorphisms.