The Boolean spectrum of a Grothendieck categoryOberseminar Darstellungstheorie

by Henning Krause (Uni Bielefeld)

Friday Jan 16, 2026, 2:15 PM → 3:15 PM Europe/Berlin

Endenicher Allee 60/1.008 - Seminarraum (Mathezentrum)

A notion of support for objects in any Grothendieck category is introduced. This is based on the spectral category of a Grothendieck category and uses its Boolean lattice of localising subcategories. The support provides a classification of all subcategories that are closed under arbitrary coproducts, subobjects, and essential extensions. There is also a notion of exact support which classifies certain thick subcategories. As an application, the coproduct decompositions of objects are described in terms of Boolean lattices. Also, for any ring Crawley-Boevey's correspondence between definable subcategories of modules and closed subsets of the Ziegler spectrum is extended.