Classifying Serre subcategories via atom spectrum
Representation Theory
2012-09-14 v2 Category Theory
Rings and Algebras
Abstract
In this paper, we introduce the atom spectrum of an abelian category as a topological space consisting of all the equivalence classes of monoform objects. In terms of the atom spectrum, we give a classification of Serre subcategories of an arbitrary noetherian abelian category. Moreover we show that the atom spectrum of a locally noetherian Grothendieck category is homeomorphic to its Ziegler spectrum.
Keywords
Cite
@article{arxiv.1112.6253,
title = {Classifying Serre subcategories via atom spectrum},
author = {Ryo Kanda},
journal= {arXiv preprint arXiv:1112.6253},
year = {2012}
}
Comments
15 pages