Recollement from DG quotients

We review a recollement for derived categories of DG categories arising from Drinfeld quotients. As an application we show that an exact sequence well-known in K-theory descends to numerical K-groups provided that either the quotient or the category we take the quotient with has a Serre functor, and if either the quotient functor preserves compactness or if the K-group of the quotient is torsion-free.Comment: 7 pages, comments are welcome. arXiv admin note: text overlap with arXiv:2105.1333