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2 results

  • p-units in ray class fields of real quadratic number fields

  • Part of
  • Hugo Chapdelaine
  • Journal:
    Compositio Mathematica / Volume 145 / Issue 2 / March 2009
    Published online by Cambridge University Press:
    01 March 2009, pp. 364-392
    Print publication:
    March 2009
    • Article
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  • Let K be a real quadratic number field and let p be a prime number which is inert in K. We denote the completion of K at the place p by Kp. We propose a p-adic construction of special elements in Kp× and formulate the conjecture that they should be p-units lying in narrow ray class fields of K. The truth of this conjecture would entail an explicit class field theory for real quadratic number fields. This construction can be viewed as a natural generalization of a construction obtained by Darmon and Dasgupta who proposed a p-adic construction of p-units lying in narrow ring class fields of K.