### Abstract

Let k be a field of characteristic zero, let X be a geometrically integral k-variety of dimension n and let K be its field of functions. We prove that, given an element α∈Hm(K,μr⊗m), there exist ^{n2} functions {fi},i=1,...,n2 such that α becomes unramified in L=K(f11/r,...,fn21/r).

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

Pages (from-to) | 173-178 |

Number of pages | 6 |

Journal | Journal of Algebra |

Volume | 377 |

DOIs | |

State | Published - Mar 1 2013 |

### Fingerprint

### Keywords

- Brauer group
- Galois cohomology
- Period-index problem
- Unramified cohomology

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

**A bound to kill the ramification over function fields.** / Pirutka, Alena.

Research output: Contribution to journal › Article

*Journal of Algebra*, vol. 377, pp. 173-178. https://doi.org/10.1016/j.jalgebra.2012.11.045

}

TY - JOUR

T1 - A bound to kill the ramification over function fields

AU - Pirutka, Alena

PY - 2013/3/1

Y1 - 2013/3/1

N2 - Let k be a field of characteristic zero, let X be a geometrically integral k-variety of dimension n and let K be its field of functions. We prove that, given an element α∈Hm(K,μr⊗m), there exist n2 functions {fi},i=1,...,n2 such that α becomes unramified in L=K(f11/r,...,fn21/r).

AB - Let k be a field of characteristic zero, let X be a geometrically integral k-variety of dimension n and let K be its field of functions. We prove that, given an element α∈Hm(K,μr⊗m), there exist n2 functions {fi},i=1,...,n2 such that α becomes unramified in L=K(f11/r,...,fn21/r).

KW - Brauer group

KW - Galois cohomology

KW - Period-index problem

KW - Unramified cohomology

UR - http://www.scopus.com/inward/record.url?scp=84871799082&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84871799082&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2012.11.045

DO - 10.1016/j.jalgebra.2012.11.045

M3 - Article

AN - SCOPUS:84871799082

VL - 377

SP - 173

EP - 178

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -