Compactly generated t-structures on the derived category of a Noetherian ring
By Leovigildo Alonso, A. Jeremias, Manuel Saor'in. 2007
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Abstract We study t -structures on D ( R ) the derived category of modules over a commutative Noetherian ring R generated by complexes in D fg − ( R ) . We prove that they are exactly the compactly generated t -structures on D ( R ) and describe them in terms of decreasing filtrations by supports of Spec ( R ) . A decreasing filtration by supports ϕ : Z → Spec ( R ) satisfies the weak Cousin condition if for any integer i , the set ϕ ( i ) contains all the immediate generalizations of each point in ϕ ( i + 1 ) . If a compactly generated t -structure on D ( R ) restricts to a t -structure on D fg ( R ) then the corresponding filtration satisfies the weak Cousin condition. If R has a pointwise dualizing complex the converse is true. If the ring R has dualizing complex then these are exactly all the t -structures on D fg b ( R ) .
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/c46884f6b681a559b406bc9af0b5bc68f520bfce
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Citations in the corpus
- Classification of resolving subcategories and grade consistent functions (2012, methodology): “That classification is essentially the same as Theorem 1.2, since one can get a descending sequence of specialization closed subsets as in [2, Definition 3.1] by taking Yi = {p ∈SpecR|f(p) ≥i}. Also in [1], a classification was obtained for compactly generated t-structures in the derived categories of ”