Classifying Serre subcategories via atom spectrum

Details Classifying Serre subcategories via atom spectrum Classifying Serre subcategories via atom spectrum

2011-12-29

arxiv.org/abs/1112.6253v1

Mathematics

Representation Theory

16 pages

Scientific paper

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.

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