Title: Vanishing theorems for the negative K-theory of stacks,
Abstract: We prove that the homotopy algebraic K-theory of tame quasi-DM stacks
satisfies cdh-descent. We apply this descent result to prove that if X is a
Noetherian tame quasi-DM stack and i < -dim(X), then K_i(X)[1/n] = 0 (resp.
K_i(X, Z/n) = 0) provided that n is nilpotent on X (resp. is invertible on X).
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.