Refining thick subcategory theorems

• Autorzy: Sunil K. Chebolu
• Języki publikacji: EN

Abstrakty

EN

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 ℂ₂ can be generated by iterated cofiberings of the Smith-Toda complex. We also discuss several consequences of these classification theorems.

Kategorie tematyczne

• 18E30: Derived categories, triangulated categories
• 55P42: Stable homotopy theory, spectra
• 18F30: Grothendieck groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2006
• Tom: 189
• Numer: 1
• Strony: 61-97

Daty

wydano

2006

Twórcy

autor

Sunil K. Chebolu

• Department of Mathematics, University of Western Ontario, London, Ontario, Canada, N6A 5B7

Identyfikatory

DOI

10.4064/fm189-1-5