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Refining thick subcategory theorems

Sunil K. Chebolu (2006)

Fundamenta Mathematicae

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...

Relative Algebraic K-Theory. An Appendix to the Paper of K.R.Coombes and V. Srinivas.

K.R. Coombes (1982/1983)

Inventiones mathematicae

Relative K-Theory and Vector Bundles on Certain Singular Varieties.

K.R. Coombes, V. Srinivas (1982/1983)

Inventiones mathematicae

Relative normalizing extensions.

Vidal Martín, C. (1996)

Bulletin of the Belgian Mathematical Society - Simon Stevin

Relative subanalytic sheaves

Teresa Monteiro Fernandes, Luca Prelli (2014)

Fundamenta Mathematicae

Given a real analytic manifold Y, denote by $Y_{s a}$ the associated subanalytic site. Now consider a product Y = X × S. We construct the endofunctor $ℱ \mapsto ℱ^{S}$ on the category of sheaves on $Y_{s a}$ and study its properties. Roughly speaking, $ℱ^{S}$ is a sheaf on $X_{s a} \times S$ . As an application, one can now define sheaves of functions on Y which are tempered or Whitney in the relative sense, that is, only with respect to X.