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Arithmetic Applications:- The Cyclotomic Case

  • Klaus W. Roggenkamp
  • Martin J. Taylor
Part of the DMV Seminar book series (OWS, volume 18)

Abstract

From now on, we fix an odd prime p and take K to be a number field containing a primitive pth root ζ of 1, and G to be a cyclic group of order p. We identify G with the group of pth roots of 1 in K. As before, we write A = KG, B = Map(G,K), and take \( mathfrak{A} and \mathfrak{B} = \mathfrak{A} D \) to be Hopf orders in these Hopf algebras. Our aim is to use the properties of certain L-functions arising in arithmetic, together with Theorem 4.2 of Chapter III, to investigate the kernel of the map ψ : \( PH(\mathfrak{B}) \to C1(\mathfrak{A} \) for certain special Hopf orders \( mathfrak{A} \) . Our results therefore concern those principal homogeneous spaces for \( mathfrak{B} \) which are isomorphic to \( mathfrak{B} as \mathfrak{A} \) -modules.

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Copyright information

© Springer Basel AG 1992

Authors and Affiliations

  • Klaus W. Roggenkamp
    • 1
  • Martin J. Taylor
    • 2
  1. 1.Mathematisches Institut BUniversität StuttgartStuttgart 80Germany
  2. 2.Dept. of Mathematics U.M.I.S.T.ManchesterEngland

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