VANISHING OF THE NEGATIVE HOMOTOPY -THEORY OF QUOTIENT SINGULARITIES
Making use of Gruson–Raynaud’s technique of ‘platification par éclatement’, Kerz and Strunk proved that the negative homotopy -theory groups of a Noetherian scheme of Krull dimension vanish below . In this article, making use of noncommutative algebraic geometry, we improve this result in the case o...
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| Format: | Article |
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Cambridge University Press (CUP)
2018
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| Online Access: | http://hdl.handle.net/1721.1/116059 https://orcid.org/0000-0001-5558-9236 |
| _version_ | 1826212809876176896 |
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| author | Trigo Neri Tabuada, Goncalo Jorge |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Trigo Neri Tabuada, Goncalo Jorge |
| author_sort | Trigo Neri Tabuada, Goncalo Jorge |
| collection | MIT |
| description | Making use of Gruson–Raynaud’s technique of ‘platification par éclatement’, Kerz and Strunk proved that the negative homotopy -theory groups of a Noetherian scheme of Krull dimension vanish below . 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 -theory groups vanish below . Furthermore, in the case of cyclic quotient singularities, we provide an explicit ‘upper bound’ for the first negative homotopy -theory group. |
| first_indexed | 2024-09-23T15:38:15Z |
| format | Article |
| id | mit-1721.1/116059 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T15:38:15Z |
| publishDate | 2018 |
| publisher | Cambridge University Press (CUP) |
| record_format | dspace |
| spelling | mit-1721.1/1160592022-10-02T03:04:59Z VANISHING OF THE NEGATIVE HOMOTOPY -THEORY OF QUOTIENT SINGULARITIES Trigo Neri Tabuada, Goncalo Jorge Massachusetts Institute of Technology. Department of Mathematics Trigo Neri Tabuada, Goncalo Jorge Making use of Gruson–Raynaud’s technique of ‘platification par éclatement’, Kerz and Strunk proved that the negative homotopy -theory groups of a Noetherian scheme of Krull dimension vanish below . 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 -theory groups vanish below . Furthermore, in the case of cyclic quotient singularities, we provide an explicit ‘upper bound’ for the first negative homotopy -theory group. 2018-06-04T17:17:51Z 2018-06-04T17:17:51Z 2017-05 2017-04 2018-05-31T16:39:50Z Article http://purl.org/eprint/type/JournalArticle 1474-7480 1475-3030 http://hdl.handle.net/1721.1/116059 Tabuada, Gonçalo. “VANISHING OF THE NEGATIVE HOMOTOPY -THEORY OF QUOTIENT SINGULARITIES.” Journal of the Institute of Mathematics of Jussieu (May 2017): 1–9 © 2017 Cambridge University Press https://orcid.org/0000-0001-5558-9236 http://dx.doi.org/10.1017/S1474748017000172 Journal of the Institute of Mathematics of Jussieu Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Cambridge University Press (CUP) arXiv |
| spellingShingle | Trigo Neri Tabuada, Goncalo Jorge VANISHING OF THE NEGATIVE HOMOTOPY -THEORY OF QUOTIENT SINGULARITIES |
| title | VANISHING OF THE NEGATIVE HOMOTOPY -THEORY OF QUOTIENT SINGULARITIES |
| title_full | VANISHING OF THE NEGATIVE HOMOTOPY -THEORY OF QUOTIENT SINGULARITIES |
| title_fullStr | VANISHING OF THE NEGATIVE HOMOTOPY -THEORY OF QUOTIENT SINGULARITIES |
| title_full_unstemmed | VANISHING OF THE NEGATIVE HOMOTOPY -THEORY OF QUOTIENT SINGULARITIES |
| title_short | VANISHING OF THE NEGATIVE HOMOTOPY -THEORY OF QUOTIENT SINGULARITIES |
| title_sort | vanishing of the negative homotopy theory of quotient singularities |
| url | http://hdl.handle.net/1721.1/116059 https://orcid.org/0000-0001-5558-9236 |
| work_keys_str_mv | AT trigoneritabuadagoncalojorge vanishingofthenegativehomotopytheoryofquotientsingularities |