# 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} }

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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