Refining thick subcategory theorems

Sunil K. Chebolu. "Refining thick subcategory theorems." Fundamenta Mathematicae 189.1 (2006): 61-97. <http://eudml.org/doc/282721>.

@article{SunilK2006,
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 ℂ₂ can be generated by iterated cofiberings of the Smith-Toda complex. We also discuss several consequences of these classification theorems.},
author = {Sunil K. Chebolu},
journal = {Fundamenta Mathematicae},
keywords = {thick subcategories; triangulated subcategory; Grothendieck group; derived category; finite spectra; Smith-Toda complex},
language = {eng},
number = {1},
pages = {61-97},
title = {Refining thick subcategory theorems},
url = {http://eudml.org/doc/282721},
volume = {189},
year = {2006},
}

TY - JOUR
AU - Sunil K. Chebolu
TI - Refining thick subcategory theorems
JO - Fundamenta Mathematicae
PY - 2006
VL - 189
IS - 1
SP - 61
EP - 97
AB - 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.
LA - eng
KW - thick subcategories; triangulated subcategory; Grothendieck group; derived category; finite spectra; Smith-Toda complex
UR - http://eudml.org/doc/282721
ER -