Vanishing of the Negative Homotopy -theory of Quotient Singularities
Year: 2017
Type: article
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.
Author: Gonçalo Tabuada
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2963557400