### 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 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

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## Cite this

Haesemeyer, C., & Weibel, C. (2018). K-theory of line bundles and smooth varieties.

*Proceedings of the American Mathematical Society*,*146*(10), 4139-4150. https://doi.org/10.1090/proc/14112