### 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 |

DOIs | |

State | Published - 2017 |

### Publication series

Name | Progress in Mathematics |
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Volume | 320 |

ISSN (Print) | 0743-1643 |

ISSN (Electronic) | 2296-505X |

### Keywords

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

### ASJC Scopus subject areas

- Analysis
- Algebra and Number Theory
- Geometry and Topology

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## Cite this

Pirutka, A. (2017). On a local-global principle for H

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