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The decomposition of primes in torsion point fields / Clemens Adelmann.

By: Material type: TextTextSeries: Lecture notes in mathematics (Springer-Verlag) ; 1761.Publication details: Berlin ; New York : Springer, ©2001.Description: 1 online resource (vi, 142 pages) : illustrationsContent type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9783540449492
  • 3540449493
Subject(s): Additional physical formats: Print version:: Decomposition of primes in torsion point fields.DDC classification:
  • 510 s 512/.4 21
LOC classification:
  • QA3 .L28 no. 1761
Online resources:
Contents:
Introduction -- Decomposition laws -- Elliptic curves -- Elliptic modular curves -- Torsion point fields -- Invariants and resolvent polynomials -- Appendix: Invariants of elliptic modular curves; L-series coefficients a p; Fully decomposed prime numbers; Resolvent polynomials; Free resolution of the invariant algebra.
Summary: We investigate the decomposition of prime ideals in non-abelian extensions of number fields. These fields are generated by the coordinates of torsion points of elliptic curves without complex multiplications. We explain the necessary prerequisites from the theory of elliptic curves, modular forms, algebraic number theory, and invariant theory. Due to the complexity of the problem, complete results are restricted to torsion points of low order. These results are complemented by computational data which also cover some unsolved cases.
Holdings
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Includes bibliographical references (pages 135-136) and index.

Introduction -- Decomposition laws -- Elliptic curves -- Elliptic modular curves -- Torsion point fields -- Invariants and resolvent polynomials -- Appendix: Invariants of elliptic modular curves; L-series coefficients a p; Fully decomposed prime numbers; Resolvent polynomials; Free resolution of the invariant algebra.

We investigate the decomposition of prime ideals in non-abelian extensions of number fields. These fields are generated by the coordinates of torsion points of elliptic curves without complex multiplications. We explain the necessary prerequisites from the theory of elliptic curves, modular forms, algebraic number theory, and invariant theory. Due to the complexity of the problem, complete results are restricted to torsion points of low order. These results are complemented by computational data which also cover some unsolved cases.

Print version record.

English.

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