A bound to kill the ramification over function fields

@article{Pirutka2011ABT,
  title={A bound to kill the ramification over function fields},
  author={Alena Pirutka},
  journal={arXiv: Number Theory},
  year={2011}
}
  • Alena Pirutka
  • Published 2011
  • Mathematics
  • arXiv: Number Theory
  • 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 fractions. Under the assumption that K contains all r-th roots of unity for an integer r, we prove that, given an element in H^m(K, Z/r), it becomes unramified in the extension of K obtained by adding r-th roots of some n^2 functions in K. 
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