Torsion classes of finite type and spectra
| dc.creator | Garkusha, Grigory | |
| dc.creator | Prest, Mike | |
| dc.date | 2006-12-15 | |
| dc.date.accessioned | 2026-07-07T07:35:23Z | |
| dc.date.available | 2026-07-07T07:35:23Z | |
| dc.description | Given a commutative ring R (respectively a positively graded commutative ring $A=\ps_{j\geq 0}A_j$ which is finitely generated as an A_0-algebra), a bijection between the torsion classes of finite type in Mod R (respectively tensor torsion classes of finite type in QGr A) and the set of all subsets Y\subset Spec R (respectively Y\subset Proj A) of the form Y=\cup_{i\inΩ}Y_i, with Spec R\Y_i (respectively Proj A\Y_i) quasi-compact and open for all i\inΩ, is established. Using these bijections, there are constructed isomorphisms of ringed spaces (Spec R,O_R)-->(Spec(Mod R),O_{Mod R}) and (Proj A,O_{Proj A})-->(Spec(QGr A),O_{QGr A}), where (Spec(Mod R),O_{Mod R}) and (Spec(QGr A),O_{QGr A}) are ringed spaces associated to the lattices L_{tor}(Mod R) and L_{tor}(QGr A) of torsion classes of finite type. Also, a bijective correspondence between the thick subcategories of perfect complexes perf(R) and the torsion classes of finite type in Mod R is established. | |
| dc.identifier | https://arxiv.org/abs/math/0612448 | |
| dc.identifier | http://arxiv.org/abs/math/0612448 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/120076 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | K-Theory and Homology | |
| dc.subject | 18E40, 18E30, 18F99 | |
| dc.title | Torsion classes of finite type and spectra | |
| dc.type | text |