VANISHING OF THE NEGATIVE HOMOTOPY K-THEORY OF QUOTIENT SINGULARITIES

Making use of Gruson–Raynaud’s technique of ‘platification par éclatement’, Kerz and Strunk proved that the negative homotopy (Formula presented.)-theory groups of a Noetherian scheme (Formula presented.) of Krull dimension (Formula presented.) vanish below (Formula presented.). In this article, making use of noncommutative algebraic geometry, we improve this result in the case of quotient singularities by proving that the negative homotopy (Formula presented.)-theory groups vanish below (Formula presented.). Furthermore, in the case of cyclic quotient singularities, we provide an explicit ‘upper bound’ for the first negative homotopy (Formula presented.)-theory group.