Aisles, Recollements And Dg Categories

The first part of this thesis is due to study the relation between recollements andaisles. Basing on [CPS] and [KV2], we show that every recollement induces a bi-aisle.Conversely, every bi-aisle induces a recollement. Similar to [KV2], for a Dynkin-algebra A, we prove that there is a bijection between the bi-aisles in Db(A) and thestrictly full triangulated subcategories of Db(A) which are closed under direct sum-mands. The second part of this thesis is due to study the t-structures on the derived cat-egory of a negative dg category. We prove that for a negative dg category A, the derivedcategory D(A) has a natural t-structure defined by the homology groups. Let H be theheart of the t-structure, then D(A) coincides with its smallest strictly full triangulatedsubcategory containing H and closed under coproducts and products. Moreover, if Ais homology bounded, then H is a set of generators of D(A).