Syzygy properties under recollements of derived categories

Let A, B and C be artin algebras such that there is a recollement of D ( Mod A ) relative to D ( Mod B ) and D ( Mod C ) . We compare the algebras A, B and C with respect to syzygy-finite properties and Igusa-Todorov properties under suitable conditions and consider relevant results in the recollements of the bounded derived categories. Further, we characterize when the functor j ⁎ (resp., i ⁎ , i ! ) in a recollement ( D b ( mod B ) , D b ( mod A ) , D b ( mod C ) , i ⁎ , i ⁎ , i ! , j ! , j ⁎ , j ⁎ ) is an eventually homological isomorphism.