VANISHING OF THE NEGATIVE HOMOTOPY K-THEORY OF QUOTIENT SINGULARITIES

Gonçalo Tabuada

doi:10.1017/S1474748017000172

VANISHING OF THE NEGATIVE HOMOTOPY K-THEORY OF QUOTIENT SINGULARITIES

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Abstract

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.

Original language	English
Pages (from-to)	1-9
Number of pages	9
Journal	Journal of the Institute of Mathematics of Jussieu
DOIs	https://doi.org/10.1017/S1474748017000172
Publication status	Published - 8 May 2017

Keywords

K-theory
noncommutative algebraic geometry
singularities

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abstract = "Making use of Gruson–Raynaud{\textquoteright}s technique of {\textquoteleft}platification par {\'e}clatement{\textquoteright}, 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 {\textquoteleft}upper bound{\textquoteright} for the first negative homotopy (Formula presented.)-theory group.",

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VANISHING OF THE NEGATIVE HOMOTOPY K-THEORY OF QUOTIENT SINGULARITIES

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