Refining thick subcategory theorems

Volume 189 / 2006

Sunil K. Chebolu Fundamenta Mathematicae 189 (2006), 61-97 MSC: Primary: 55P42, 18E30, 18F30. DOI: 10.4064/fm189-1-5

Abstract

We use a $K$-theory recipe of Thomason to obtain classifications of triangulated subcategories via refining some standard thick subcategory theorems. We apply this recipe to the full subcategories of finite objects in the derived categories of rings and the stable homotopy category of spectra. This gives, in the derived categories, a complete classification of the triangulated subcategories of perfect complexes over some commutative rings. In the stable homotopy category of spectra we obtain only a partial classification of the triangulated subcategories of the finite $p$-local spectra. We use this partial classification to study the lattice of triangulated subcategories. This study gives some new evidence for a conjecture of Adams that the thick subcategory $\mathbb C_2$ can be generated by iterated cofiberings of the Smith–Toda complex. We also discuss several consequences of these classification theorems.

Authors

  • Sunil K. CheboluDepartment of Mathematics
    University of Western Ontario
    London, Ontario
    Canada, N6A 5B7
    e-mail

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