VANISHING OF THE NEGATIVE HOMOTOPY -THEORY OF QUOTIENT SINGULARITIES
2017 ◽
Vol 18
(3)
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pp. 619-627
Keyword(s):
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.
1990 ◽
Vol 107
(1)
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pp. 91-101
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2009 ◽
Vol 213
(6)
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pp. 1086-1096
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1988 ◽
Vol 53
(1)
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pp. 284-293
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Keyword(s):
2017 ◽
Vol 69
(2)
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pp. 509-548
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2008 ◽
Vol 136
(08)
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pp. 2745-2747
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2010 ◽
Vol 101
(2)
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pp. 554-588
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2015 ◽
Vol 17
(11)
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pp. 2805-2842
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