Arithmetic Applications:- The Elliptic Case

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


In this final chapter, we will discuss two ways in which our algebraic machinery gives connections between certain L-functions and the Galois module structure of extensions arising from elliptic curves with complex multiplication. The first of these, which we will describe only briefly, is analogous to the cyclotomic result of the previous chapter, and the second concerns the implications of the conjecture of Birch and Swinnerton-Dyer for Galois module structure. Much, but not all, of the content of this chapter can be extended to abelian varieties with complex multiplication.


Elliptic Curve Elliptic Curf Abelian Variety Good Reduction Galois Cohomology 
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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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