Classifying torsion pairs for tame hereditary algebras and tubes

2014 ◽  
pp. 163-178
Author(s):  
Aslak Buan
Keyword(s):  
Hereditary Algebras ◽  
Torsion Pairs ◽  
Tame Hereditary Algebras

scholarly journals Parametrizing torsion pairs in derived categories

2021 ◽  
Vol 25 (23) ◽  
pp. 679-731
Author(s):  
Lidia Angeleri Hügel ◽  
Michal Hrbek
Keyword(s):  
Natural Extension ◽  
Commutative Rings ◽  
Derived Categories ◽  
Derived Category ◽  
Content Type ◽  
Finite Dimensional ◽  
Hereditary Algebras ◽  
Torsion Pairs ◽  
Zariski Spectrum ◽  
Compactly Generated

We investigate parametrizations of compactly generated t-structures, or more generally, t-structures with a definable coaisle, in the unbounded derived category D ( M o d - A ) \mathrm {D}({\mathrm {Mod}}\text {-}A) of a ring A A . To this end, we provide a construction of t-structures from chains in the lattice of ring epimorphisms starting in A A , which is a natural extension of the construction of compactly generated t-structures from chains of subsets of the Zariski spectrum known for the commutative noetherian case. We also provide constructions of silting and cosilting objects in D ( M o d - A ) \mathrm {D}({\mathrm {Mod}}\text {-}A) . This leads us to classification results over some classes of commutative rings and over finite dimensional hereditary algebras.

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