VANISHING OF THE NEGATIVE HOMOTOPY $K$-THEORY OF QUOTIENT SINGULARITIES. (8th May 2017)

• Record Type: Journal Article
• Authors: Tabuada, Gonçalo
• Is Part Of: Journal of the Institute of Mathematics of Jussieu. Volume 18:Number 3(2019)
• Page Start: 619
• Page End: 627
• Publication Date: 2017-05-08
• Subjects: 14A22, -- 14B05, -- 14H20, -- 19E08, -- 19D35; K-theory, -- singularities, -- noncommutative algebraic geometry; Mathematics -- Periodicals; 510.5
• DOI: 10.1017/S1474748017000172
• Languages: English
• ISSNs: 1474-7480

Abstract

Abstract : Making use of Gruson–Raynaud's technique of 'platification par éclatement', 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 article, 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.