scholarly journals Iwasawa theory for elliptic curves over imaginary quadratic fields

2001 ◽  
Vol 13 (1) ◽  
pp. 1-25 ◽  
Author(s):  
Massimo Bertolini
Keyword(s):  
Elliptic Curves ◽  
Iwasawa Theory ◽  
Quadratic Fields ◽  
Imaginary Quadratic Fields

scholarly journals Truncated Euler Systems over Imaginary Quadratic Fields

2009 ◽  
Vol 195 ◽  
pp. 97-111
Author(s):  
Soogil Seo
Keyword(s):  
Class Group ◽  
Quadratic Field ◽  
Abelian Extension ◽  
Iwasawa Theory ◽  
Quadratic Fields ◽  
Galois Module ◽  
Imaginary Quadratic Fields ◽  
Euler Systems ◽  
Graded Module ◽  
Elliptic Units

AbstractLet K be an imaginary quadratic field and let F be an abelian extension of K. It is known that the order of the class group ClF of F is equal to the order of the quotient UF/ElF of the group of global units UF by the group of elliptic units ElF of F. We introduce a filtration on UF/ElF made from the so-called truncated Euler systems and conjecture that the associated graded module is isomorphic, as a Galois module, to the class group. We provide evidence for the conjecture using Iwasawa theory.

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