In several ways, the algebraic K-theory of a height n ring simpli fies after localization at a telescope T(n+ 1). For us, the most fundamental will be Land–Mathew–Meier–Tamme purity, which is intimately tied to Clausen–Mathew–Naumann–Noel descent. The speaker will explain the purity theorem from [LMMT20], which states that LT(n+1)K(R) ≃ LT(n+1)K(LT(n)⊕T(n+1)R), and may sketch a few ingredients of the proof. The most basic example of purity is Mitchell’s theorem, which states that LT(n+1)K(R) = 0 whenever 1 R is a discrete ring and n ≥ 1; the speaker will note how this simplifies the use of the Dundas–Goodwillie–McCarthy theorem.