The central sheaf of a Grothendieck category

Journal article

The center Z(A) of an abelian category A is the endomorphism ring of the identity functor on that category. A localizing subcategory of a Grothendieck category C is said to be stable if it is stable under essential extensions. The set L^st(C) of stable localizing subcategories of C is partially ordered under reverse inclusion. We show L→Z(C/L) defines a sheaf of commutative rings on L^st(C) with respect to finite coverings. When C is assumed to be locally noetherian, we also show that the sheaf condition holds for arbitrary coverings.

Authors: Ardakov, K; Schneider, P

• Publication status: Accepted
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: Selecta Mathematica (New Series)
• Acceptance date: 2026-02-24
• EISSN: 1420-9020
• ISSN: 1022-1824
• Language: English