On the &lt;i&gt;K&lt;/i&gt;-theory of Toric Stack Bundles

Jiang, Yunfeng; Tseng, Hsian-Hua

doi:10.4310/ajm.2010.v14.n1.a1

Cited by 3 publications

(7 citation statements)

References 19 publications

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“…When G is the trivial group, the Grothendieck group K 0 (X), was computed in [32,Theorem 1.2(iii)]. When [X/G] is a Deligne-Mumford stack, a computation of K 0 (X) appears in [19].…”

Section: Overview Of the Main Resultsmentioning

confidence: 99%

“…In this case, each fiber of ⇡ is the toric stack [X/G] in the sense of [14]. If [X/G] is a Deligne-Mumford stack, this construction recovers the notion of toric stack bundles used in [19].…”

Section: Toric Stack Bundlesmentioning

confidence: 87%

“…They computed the Grothendieck group of a toric bundle over a smooth base scheme. A description of the Grothendieck group of toric Deligne-Mumford stack bundles was given by Jiang and Tseng in [19].…”

Section: Toric Stack Bundles and The Stacky Leray-hirsch Theoremmentioning

confidence: 99%

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Higher K-theory of toric stacks

Joshua¹,

Krishna²

2015

Annali Scuola Normale Superiore - Classe Di Scienze

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In this paper we develop several techniques for computing the higher G-theory and K-theory of quotient stacks. Our main results for computing these groups are in terms of spectral sequences. We show that these spectral sequences degenerate in the case of many toric stacks, thereby providing an efficient computation of their higher K-theory.We apply our main results to give an explicit description for the higher Ktheory of many quotient stacks, including smooth toric stacks. We also show that our techniques apply to compute the higher K-theory of all spherical varieties over fields of characteristic 0 and all projective smooth spherical varieties over fields of arbitrary characteristics. As another application, we describe the higher K-theory of toric stack bundles over smooth base schemes.

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“…When G is the trivial group, the Grothendieck group K 0 (X), was computed in [32,Theorem 1.2(iii)]. When [X/G] is a Deligne-Mumford stack, a computation of K 0 (X) appears in [19].…”

Section: Overview Of the Main Resultsmentioning

confidence: 99%

Section: Toric Stack Bundlesmentioning

confidence: 87%

See 1 more Smart Citation

Higher K-theory of toric stacks

Joshua¹,

Krishna²

2015

Annali Scuola Normale Superiore - Classe Di Scienze

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“…The integral version of this result for certain type of toric Deligne-Mumford stacks is due to Jiang and Tseng [25], and Iwanari [22]. Jiang and Tseng also extend some of these results to certain toric stack bundles in [24] and [26]. Borisov and Horja [5] computed the integral Grothendieck ring K 0 (X) of a toric Deligne-Mumford stack X.…”

Section: Introductionmentioning

confidence: 98%

“…When G is the trivial group, the Grothendieck group K 0 (X), was computed in [38,Theorem 1.2(iii)]. When [X/G] is a Deligne-Mumford stack, a computation of K 0 (X) appears in [26].…”

Section: Introductionmentioning

confidence: 99%

Higher K-theory of Toric stacks

Joshua¹,

Krishna²

2012

Preprint

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In this paper, we develop several techniques for computing the higher G-theory and K-theory of quotient stacks. Our main results for computing these groups are in terms of spectral sequences. We show that these spectral sequences degenerate in the case of many toric stacks, thereby providing an efficient computation of their higher K-theory. We apply our main results to give explicit description for the higher K-theory for many smooth toric stacks. As another application, we describe the higher K-theory of toric stack bundles over smooth base schemes.

show abstract