Let A be a Grothendieck category.Theλ-pure singularity category D_(λ-sg)^(b)(A)of A is a Verdier quotient of the boundedλ-pure derived category D_(λ)^(b)(A)by a thick subcategory K^(b)(PPλ),i.e.,D_(λ-sg)^(b)(A):...Let A be a Grothendieck category.Theλ-pure singularity category D_(λ-sg)^(b)(A)of A is a Verdier quotient of the boundedλ-pure derived category D_(λ)^(b)(A)by a thick subcategory K^(b)(PPλ),i.e.,D_(λ-sg)^(b)(A):=D_(λ)^(b)(A)/K b(PPλ).We mainly verify that D_(λ-sg)^(b)(A)is triangle equivalent to another quotient category under a special condition.And we also prove that a triangle equivalence between special homotopy categories induces aλ-pure derived equivalence,and it induces aλ-pure singular equivalence too.展开更多
文摘Let A be a Grothendieck category.Theλ-pure singularity category D_(λ-sg)^(b)(A)of A is a Verdier quotient of the boundedλ-pure derived category D_(λ)^(b)(A)by a thick subcategory K^(b)(PPλ),i.e.,D_(λ-sg)^(b)(A):=D_(λ)^(b)(A)/K b(PPλ).We mainly verify that D_(λ-sg)^(b)(A)is triangle equivalent to another quotient category under a special condition.And we also prove that a triangle equivalence between special homotopy categories induces aλ-pure derived equivalence,and it induces aλ-pure singular equivalence too.
