Torsion Classes of Finite Type and Spectra
نویسنده
چکیده
Given a commutative ring R (respectively a positively graded commutative ring A = ⊕j>0Aj which is finitely generated as an A0-algebra), a bijection between the torsion classes of finite type in ModR (respectively tensor torsion classes of finite type in QGrA) and the set of all subsets Y ⊆ Spec R (respectively Y ⊆ Proj A) of the form Y = S i∈Ω Yi, with Spec R \ Yi (respectively Proj A \ Yi) quasi-compact and open for all i ∈ Ω, is established. Using these bijections, there are constructed isomorphisms of ringed spaces (Spec R, OR) ∼ −→ (Spec(ModR), OModR) and (Proj A, OProj A) ∼ −→ (Spec(QGrA), OQGrA), where (Spec(ModR), OMod R) and (Spec(QGrA), OQGrA) are ringed spaces associated to the lattices Ltor(ModR) and Ltor(QGrA) of torsion classes of finite type. Also, a bijective correspondence between the thick subcategories of perfect complexes Dper(R) and the torsion classes of finite type in ModR is established.
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