We prove that the homotopy algebraic -theory of tame quasi-DM stacks satisfies cdh-descent. We apply this descent result to prove that if is a Noetherian tame quasi-DM stack and , then if is nilpotent on and if is invertible on . Our descent and vanishing results apply more generally to certain Artin stacks whose stabilizers are extensions of finite group schemes by group schemes of multiplicative type.
"Vanishing theorems for the negative $K$-theory of stacks." Ann. K-Theory 4 (3) 439 - 472, 2019. https://doi.org/10.2140/akt.2019.4.439