### Abstract

We give a K-theoretic criterion for a quasi-projective variety to be smooth. If L is a line bundle corresponding to an ample invertible sheaf on X, it suffices that K_{q} (X) ≅ K_{q} (L) for all q ≤ dim(X) +1.

Original language | English (US) |
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Pages (from-to) | 4139-4150 |

Number of pages | 12 |

Journal | Proceedings of the American Mathematical Society |

Volume | 146 |

Issue number | 10 |

DOIs | |

State | Published - Jan 1 2018 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*146*(10), 4139-4150. https://doi.org/10.1090/proc/14112

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*Proceedings of the American Mathematical Society*, vol. 146, no. 10, pp. 4139-4150. https://doi.org/10.1090/proc/14112

**K-theory of line bundles and smooth varieties.** / Haesemeyer, C.; Weibel, C.

Research output: Contribution to journal › Article

TY - JOUR

T1 - K-theory of line bundles and smooth varieties

AU - Haesemeyer, C.

AU - Weibel, C.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - We give a K-theoretic criterion for a quasi-projective variety to be smooth. If L is a line bundle corresponding to an ample invertible sheaf on X, it suffices that Kq (X) ≅ Kq (L) for all q ≤ dim(X) +1.

AB - We give a K-theoretic criterion for a quasi-projective variety to be smooth. If L is a line bundle corresponding to an ample invertible sheaf on X, it suffices that Kq (X) ≅ Kq (L) for all q ≤ dim(X) +1.

UR - http://www.scopus.com/inward/record.url?scp=85051404032&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85051404032&partnerID=8YFLogxK

U2 - 10.1090/proc/14112

DO - 10.1090/proc/14112

M3 - Article

AN - SCOPUS:85051404032

VL - 146

SP - 4139

EP - 4150

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 10

ER -