Ramification Groups of Nonabelian Kummer Extensions

  title={Ramification Groups of Nonabelian Kummer Extensions},
  author={Romyar T. Sharifi},
  journal={Journal of Number Theory},
  • R. Sharifi
  • Published 1 July 1997
  • Mathematics
  • Journal of Number Theory
Abstract The reciprocity law of Coleman for the Hilbert norm residue symbol has allowed the computation of the conductors of the abelian Kummer extensions Q p ( a ,ζ p n )/ Q p (ζ p n ) witha∈Qpandζpna primitive (pn)th root of unity for a fixed primepand all positive integersn. From these conductors, we compute the ramification groups of the nonabelian Kummer extension Q p ( Q × p )/ Q p obtained from adjoining toQpallp-power roots of its elements. More generally, given a similar nonabelian… 


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