A bound to kill the ramification over function fields

Details A bound to kill the ramification over function fields A bound to kill the ramification over function fields

2011-05-19

arxiv.org/abs/1105.3942v1

Mathematics

Number Theory

Scientific paper

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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