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1NotationandPreliminariesThroughoutpwilldenoteanoddprimeandZprespectivelyQpwilldenotetheringofpadicintegersrespthe eldofpadicnumbersGivenanynumber eldweshalldenotebycycthecyclotomicZpexte

1.NotationandPreliminariesThroughout pwilldenoteanoddprimeandZp(respectivelyQp) willdenotetheringofp-adicintegers(resp.the eldofp-adicnumbers).Givenanynumber eld weshalldenotebycycthecyclotomicZp-exte

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