EVENT DETAILS AND ABSTRACT

Title: A K-theoretic approach for refining the chromatic towers
Speaker: Sunil Chebolu
Speaker Info: University of Washington
Brief Description:
Special Note:
Abstract:

The classification of the thick subcategories (chromatic tower) of finite spectra due to Hopkins and Smith has had a tremendous impact on stable homotopy theory. For example, using this theorem, Hopkins and Smith were able to settle the class-invariance conjecture of Ravenel which classified the Bousfield classes of finite spectra. In this talk, I will explain how one can get a refinement of their chromatic tower using a K-theory recipe of Thomason. (The refinement is a classification of triangulated subcategories of finite spectra.) This approach is general enough that it applies to any triangulated category. In particular, this also gives such refinements of chromatic towers in some algebraic stable homotopy categories like the derived categories of rings and the stable module categories of group algebras. If time permits, I will show how some of this work leads naturally to Krull-Schmidt decompositions of thick subcategories in these exotic worlds.