The Decomposition of Primes in Torsion Point Fields

• Main Author: Adelmann, Clemens (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2001.
• Edition: 1st ed. 2001.
• Series: Lecture Notes in Mathematics, 1761
• Subjects: Number theory.; Algebraic geometry.; Number Theory.; Algebraic Geometry.

It is an historical goal of algebraic number theory to relate all algebraic extensionsofanumber?eldinauniquewaytostructuresthatareexclusively described in terms of the base ?eld. Suitable structures are the prime ideals of the ring of integers of the considered number ?eld. By examining the behaviou...

Table of 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.