A01=Karl Rubin
Abelian extension
Abelian variety
Absolute Galois group
Algebraic closure
Author_Karl Rubin
Barry Mazur
Big O notation
Birch and Swinnerton-Dyer conjecture
Cardinality
Category=PBH
Category=PBMW
Class field theory
Coefficient
Cohomology
Complex multiplication
Conjecture
Corollary
Cyclotomic field
Dimension (vector space)
Divisibility rule
Eigenvalues and eigenvectors
Elliptic curve
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Error term
Euler product
Euler system
Exact sequence
Existential quantification
Field of fractions
Finite set
Functional equation
Galois cohomology
Galois group
Galois module
Gauss sum
Global field
Heegner point
Ideal class group
Integer
Inverse limit
Inverse system
Karl Rubin
Local field
Mathematical induction
Maximal ideal
Modular curve
Modular elliptic curve
Natural number
Orthogonality
P-adic number
Pairing
Principal ideal
R-factor (crystallography)
Ralph Greenberg
Remainder
Residue field
Ring of integers
Scientific notation
Selmer group
Subgroup
Tate module
Taylor series
Tensor product
Theorem
Upper and lower bounds
Victor Kolyvagin
Product details
- ISBN 9780691050768
- Weight: 340g
- Dimensions: 197 x 254mm
- Publication Date: 21 May 2000
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
Secure
checkout
Fast Shipping
Easy returns
One of the most exciting new subjects in Algebraic Number Theory and Arithmetic Algebraic Geometry is the theory of Euler systems. Euler systems are special collections of cohomology classes attached to p-adic Galois representations. Introduced by Victor Kolyvagin in the late 1980s in order to bound Selmer groups attached to p-adic representations, Euler systems have since been used to solve several key problems. These include certain cases of the Birch and Swinnerton-Dyer Conjecture and the Main Conjecture of Iwasawa Theory. Because Selmer groups play a central role in Arithmetic Algebraic Geometry, Euler systems should be a powerful tool in the future development of the field. Here, in the first book to appear on the subject, Karl Rubin presents a self-contained development of the theory of Euler systems. Rubin first reviews and develops the necessary facts from Galois cohomology. He then introduces Euler systems, states the main theorems, and develops examples and applications. The remainder of the book is devoted to the proofs of the main theorems as well as some further speculations.
The book assumes a solid background in algebraic Number Theory, and is suitable as an advanced graduate text. As a research monograph it will also prove useful to number theorists and researchers in Arithmetic Algebraic Geometry.
Karl Rubin, Professor of Mathematics at Stanford University, was awarded the Cole Prize of the American Mathematical Society in 1992. He has been a Guggenheim Fellow, a Sloan Fellow, and a National Science Foundation Presidential Young Investigator.
