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The derived category of the projective line
Henning Krause, Greg Stevenson
We examine the localizing subcategories of the derived category of quasi-coherent sheaves on the projective line over a field. We provide a complete classification of all such subc…
Complete Boolean algebras are Bousfield lattices
Greg Stevenson
Given a complete Heyting algebra we construct an algebraic tensor triangulated category whose Bousfield lattice is the Booleanization of the given Heyting algebra. As a consequence…
Enrichment and representability for triangulated categories
Johan Steen, Greg Stevenson
Given a fixed tensor triangulated category S we consider triangulated categories T together with an S-enrichment which is compatible with the triangulated structure of T. It is sho…
The local-to-global principle for triangulated categories via dimension functions
Greg Stevenson
We formulate a general abstract criterion for verifying the local-to-global principle for a rigidly-compactly generated tensor triangulated category. Our approach is based upon an…