### Abstract

Let K be the function field of a smooth projective surface S over a finite field F. In this article, following the work of Parimala and Suresh, we establish a local-global principle for the divisibility of elements in H^{3}(K, ℤ/ℓ) by elements in H^{2}(K, ℤ/ℓ),l≠car.K.

Original language | English (US) |
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Title of host publication | Progress in Mathematics |

Publisher | Springer Basel |

Pages | 219-230 |

Number of pages | 12 |

Volume | 320 |

DOIs | |

State | Published - 2017 |

### Publication series

Name | Progress in Mathematics |
---|---|

Volume | 320 |

ISSN (Print) | 0743-1643 |

ISSN (Electronic) | 2296-505X |

### Fingerprint

### Keywords

- Galois cohomology
- Local global principles
- Ramification
- Surfaces over finite fields
- Unramified cohomology

### ASJC Scopus subject areas

- Algebra and Number Theory
- Analysis
- Geometry and Topology

### Cite this

^{3}of function fields of surfaces over a finite field. In

*Progress in Mathematics*(Vol. 320, pp. 219-230). (Progress in Mathematics; Vol. 320). Springer Basel. https://doi.org/10.1007/978-3-319-46852-5_10

**On a local-global principle for H ^{3}of function fields of surfaces over a finite field.** / Pirutka, Alena.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

^{3}of function fields of surfaces over a finite field. in

*Progress in Mathematics.*vol. 320, Progress in Mathematics, vol. 320, Springer Basel, pp. 219-230. https://doi.org/10.1007/978-3-319-46852-5_10

^{3}of function fields of surfaces over a finite field. In Progress in Mathematics. Vol. 320. Springer Basel. 2017. p. 219-230. (Progress in Mathematics). https://doi.org/10.1007/978-3-319-46852-5_10

}

TY - CHAP

T1 - On a local-global principle for H3of function fields of surfaces over a finite field

AU - Pirutka, Alena

PY - 2017

Y1 - 2017

N2 - Let K be the function field of a smooth projective surface S over a finite field F. In this article, following the work of Parimala and Suresh, we establish a local-global principle for the divisibility of elements in H3(K, ℤ/ℓ) by elements in H2(K, ℤ/ℓ),l≠car.K.

AB - Let K be the function field of a smooth projective surface S over a finite field F. In this article, following the work of Parimala and Suresh, we establish a local-global principle for the divisibility of elements in H3(K, ℤ/ℓ) by elements in H2(K, ℤ/ℓ),l≠car.K.

KW - Galois cohomology

KW - Local global principles

KW - Ramification

KW - Surfaces over finite fields

KW - Unramified cohomology

UR - http://www.scopus.com/inward/record.url?scp=85019668023&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85019668023&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-46852-5_10

DO - 10.1007/978-3-319-46852-5_10

M3 - Chapter

VL - 320

T3 - Progress in Mathematics

SP - 219

EP - 230

BT - Progress in Mathematics

PB - Springer Basel

ER -