Classifying subcategories, local algebra and the Rosenberg spectrum of a locally noetherian category

Abstract

Let $\mathcal{A}$ be a locally noetherian Grothendieck category. In this paper, we study subcategories of $\mathcal{A}$ using subsets of the Rosenberg spectrum $\mathfrak{S}pec(\mathcal{A})$. Along the way, we also develop results in local algebra with respect to the category $\mathcal{A}$ that we believe to be of independent interest.

Paper heavily updated

References in corpus (4)

• Derived equivalences induced by big cotilting modules
• Specialization orders on atom spectra of Grothendieck categories
• Extension groups between atoms and objects in locally noetherian Grothendieck category
• Classification of categorical subspaces of locally noetherian schemes