### Abstract

Let p be an odd prime and let k be a field finitely generated over the finite field with p elements. For any K3 surface X over k, we prove that the cokernel of the natural map Br(k)→Br(X) is finite modulo the p-primary torsion subgroup.

Original language | English (US) |
---|---|

Pages (from-to) | 11404-11418 |

Number of pages | 15 |

Journal | International Mathematics Research Notices |

Volume | 2015 |

Issue number | 21 |

DOIs | |

State | Published - Jan 1 2015 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*International Mathematics Research Notices*,

*2015*(21), 11404-11418. https://doi.org/10.1093/imrn/rnv030

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*International Mathematics Research Notices*, vol. 2015, no. 21, pp. 11404-11418. https://doi.org/10.1093/imrn/rnv030

**A finiteness theorem for the Brauer group of K3 surfaces in odd characteristic.** / Skorobogatov, Alexei N.; Zarkhin, Yuriy G.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A finiteness theorem for the Brauer group of K3 surfaces in odd characteristic

AU - Skorobogatov, Alexei N.

AU - Zarkhin, Yuriy G.

PY - 2015/1/1

Y1 - 2015/1/1

N2 - Let p be an odd prime and let k be a field finitely generated over the finite field with p elements. For any K3 surface X over k, we prove that the cokernel of the natural map Br(k)→Br(X) is finite modulo the p-primary torsion subgroup.

AB - Let p be an odd prime and let k be a field finitely generated over the finite field with p elements. For any K3 surface X over k, we prove that the cokernel of the natural map Br(k)→Br(X) is finite modulo the p-primary torsion subgroup.

UR - http://www.scopus.com/inward/record.url?scp=84975728163&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84975728163&partnerID=8YFLogxK

U2 - 10.1093/imrn/rnv030

DO - 10.1093/imrn/rnv030

M3 - Article

VL - 2015

SP - 11404

EP - 11418

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

SN - 1073-7928

IS - 21

ER -