The Decomposition of Primes in Torsion Point Fields
Edition: 1 edition
Publisher: Springer
Published: June 15, 2001
Language: eng
Format: Paperback
Number of pages: 142
ISBN-13: 9783540420354
Subjects: Algebraic Geometry; Fields & rings; Number Theory; Ideals (Algebra); Algebraic Number Theory; Mathematics; Torsion theory (Algebra); Science/Mathematics; Algebra - General; General; Mathematics / Number Theory; Geometry - Algebraic; Decomposition (Mathematics)
First sentence: It is an historical goal of algebraic number theory to relate all algebraic extensions of a number field in a unique way to structures that are exclusively described in terms of the base field.
Description: 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.
Notes: Lecture Notes in Mathematics