HEREDITARY TORSION THEORIES OF A LOCALLY NOETHERIAN GROTHENDIECK CATEGORY

Let A be a locally noetherian Grothendieck category. We construct closure operators on the lattice of subcategories of A and the lattice of subsets of ASpec A in terms of associated atoms. This establishes a one-to-one correspondence between hereditary torsion theories of A and closed subsets of ASpec A. If A is locally stable, then the hereditary torsion theories can be studied locally. In this case, we show that the topological space ASpec A is Alexandroff.