Vanishing of the negative homotopy K-theory of quotient singularities

Goncalo Tabuada

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arXiv · 1608.08213

Vanishing of the negative homotopy K-theory of quotient singularities

Goncalo Tabuada

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Abstract

Making use of Gruson-Raynaud's technique of "platification par eclatement", Kerz and Strunk proved that the negative homotopy K-theory groups of a Noetherian scheme X of Krull dimension d vanish below -d. In this note, making use of noncommutative algebraic geometry, we improve this result in the case of quotient singularities by proving that the negative homotopy K-theory groups vanish below -1. Furthermore, in the case of cyclic quotient singularities, we provide an explicit "upper bound" for the first negative homotopy K-theory group.

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Goncalo Tabuada. 2016-08-29. Vanishing of the negative homotopy K-theory of quotient singularities. https://arxiv.org/abs/1608.08213

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