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Preprint Number 29

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29. Grigory Garkusha and Mike Prest
Torsion classes of finite type and spectra
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Abstract:

Given a commutative ring R (respectively a positively graded commutative ring A which is finitely generated over its 0-component), a bijection is established between the finite type torsion classes of R-modules (respectively tensor torsion classes of finite type in QGr A) and the set of all subsets of spec R (respectivelyof Proj A) which are unions of complements of quasi-compact open subsets. Using these bijections, isomorphisms of related ringed spaces are constructed. Also, a bijective correspondence between the thick subcategories of perfect complexes of R-modules and the finite type torsion classes of R-modules is established.

Mathematics Subject Classification: 03 16 18

Keywords and phrases: affine scheme, projective scheme, commutative ring, graded ring, torsion class, finite type, spectrum, thick subcategory.

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